✓ Effortless Math · Free Tool

Integral Calculator

Enter a polynomial in x to find its antiderivative term-by-term with the power rule, compute the definite integral on [a, b] via the Fundamental Theorem, shade the area under the curve, and see full step-by-step working. Switch to numeric mode for any function f(x).

Power rule:  ∫ a·xⁿ dx = a·xⁿ⁺¹ / (n+1) + C
∫ f(x) dx,  f(x) = function from  a = lower (optional) to  b = upper (optional)

Polynomial mode: type a polynomial like 9x^2 - 4x + 5. Use ^ for powers. Give both bounds a and b to compute a definite integral, or leave them blank for just the antiderivative + C.

Results

Antiderivative
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Antiderivative — F(x) + C
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Definite integral
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Bounds [a, b]
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Method
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Graph

f(x)area on [a, b]

Step-by-step (power rule + FTC)