About the Integral Calculator
An integral adds up a quantity continuously, and it gives the area under a curve. For a polynomial, the rule is the reverse of the one for derivatives: raise each power by one and divide by the new power. This calculator gives the indefinite integral, with the constant C, and if you enter two limits, the exact value of the definite integral between them. Type a polynomial in x and, optionally, a lower and an upper limit and the integral of a polynomial appears at once, with a few related figures underneath, and you can copy the result with one tap. The sums run in your browser, so nothing you enter is uploaded.
Updated October 2026
How to use the Integral Calculator
- 1Enter a polynomial in x and, optionally, a lower and an upper limit.
- 2Pick the units or options from the menus if the integral of a polynomial tool offers them.
- 3Read the integral of a polynomial in the large result box.
- 4Look at the extra rows for related figures.
- 5Press Copy result to keep the answer.
When you need the integral of a polynomial
Integrals measure the area under a graph, the distance travelled from a speed curve, the work done by a changing force and the total of any rate. Students use them to check calculus work, and engineers use the same rule to total quantities that vary smoothly.
The answer for the indefinite integral always has + C because many functions have the same derivative; they differ by a constant. The definite integral removes C, since it cancels in the subtraction.
How the integral of a polynomial is worked out
Power rule: the integral of c·xⁿ is c·xⁿ⁺¹ ÷ (n + 1) + C. A definite integral from a to b is F(b) − F(a), where F is the antiderivative. The integral of 3x² + 2x − 5 is x³ + x² − 5x + C. Between x = 0 and x = 2, the value is (8 + 4 − 10) − 0 = 2. The integral of 2x² is (2/3)x³ + C, and the integral of the constant 4 is 4x + C.
Every answer on this page comes from that one rule, so you can check any result by hand with a calculator. The figures shown underneath, such as other units, are conversions of the same answer.
- Antiderivative with + C
- Definite integral between limits
- Fractions kept exact for whole numbers
Mistakes to avoid with integral of a polynomial
A definite integral is a signed area: parts of the curve below the x-axis count as negative, so the value can be smaller than the geometric area. If you want the total area, split the range at the points where the curve crosses the axis.
On phone and computer
On a phone, type into the boxes one after another and read the integral of a polynomial underneath; Copy result puts it on the clipboard for a message or a note. On a computer the inputs sit on the left and the answer on the right, so you can change one figure and watch the integral of a polynomial move. The integral calculator works the same on both. An integral often leads to a second question about slopes or areas. Check the rate of change with the Derivative Calculator, find a simple shape's size with the Area Calculator, and solve the equation for the limits with the Quadratic Equation Solver.
Features
- Signed area
- Split at axis crossings
- Constant C disappears in definite integrals
- Clear messages when the integral of a polynomial inputs make no sense
- Copy the result with one tap
- Private: nothing is uploaded
Frequently asked questions
How do I calculate integral of a polynomial?
Power rule: the integral of c·xⁿ is c·xⁿ⁺¹ ÷ (n + 1) + C. A definite integral from a to b is F(b) − F(a), where F is the antiderivative. The integral of 3x² + 2x − 5 is x³ + x² − 5x + C. Between x = 0 and x = 2, the value is (8 + 4 − 10) − 0 = 2. The integral of 2x² is (2/3)x³ + C, and the integral of the constant 4 is 4x + C.
What is the formula for integral of a polynomial?
Power rule: the integral of c·xⁿ is c·xⁿ⁺¹ ÷ (n + 1) + C. A definite integral from a to b is F(b) − F(a), where F is the antiderivative. The integral calculator applies it exactly and rounds only the displayed answer to six significant figures.
What does C mean?
The constant of integration. It stands for any constant, because the derivative of a constant is zero.
Can the integral be negative?
Yes, when more of the curve lies below the axis than above it.
How do I get the area between two curves?
Integrate the difference of the two functions between the points where they meet.
Is this integral calculator free and private?
Yes. It is free, needs no account and runs in your browser, so the numbers you type are not uploaded or stored.