Integral Calculator — Antiderivative & Definite Integral (Free)

Use this free integral calculator to integrate a function. Enter a polynomial to get its antiderivative (with + C) by the power rule, add bounds to evaluate a definite integral F(b) − F(a), or use numeric mode to integrate any function on an interval with Simpson’s rule.

How to use the integral calculator

1. Enter a polynomial in x (or switch to numeric mode for any function).
2. Optionally enter lower and upper bounds for a definite integral.
3. Press Calculate to see the antiderivative, the value, and the steps.

The power rule for integrals

Integrating a power adds one to the exponent: ∫a·xⁿ dx = a·xⁿ⁺¹/(n+1) + C. For a definite integral, the Fundamental Theorem of Calculus gives the value as F(b) − F(a).

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Frequently asked questions

How do you integrate a polynomial?

Apply the power rule to each term: ∫a·xⁿ dx = a·xⁿ⁺¹/(n+1), then add the constant of integration C.

What is a definite integral?

The signed area under the curve between two x-values, computed as F(b) − F(a) where F is an antiderivative.

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Can it integrate non-polynomials?

Yes — numeric mode uses Simpson’s rule to approximate the definite integral of any function on the interval you choose.

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Read the full lesson: learn the method step by step.

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