∫ Integral Calculator
Enter the coefficients of a polynomial up to degree 3 plus a lower and upper bound, and this tool finds the antiderivative and the definite integral.
What this calculator does
This tool integrates a polynomial function f(x) = ax³ + bx² + cx + d. It reports both the general antiderivative F(x) and the definite integral of f(x) between the lower and upper bounds you enter, which represents the net signed area under the curve.
The method: the reverse power rule
Each term is integrated using ∫xⁿ dx = xⁿ⁺¹ / (n+1) + C, giving F(x) = (a/4)x⁴ + (b/3)x³ + (c/2)x² + dx. The definite integral is then computed with the Fundamental Theorem of Calculus as F(upper) − F(lower); the constant C cancels out automatically.
- Set higher-degree coefficients to 0 to integrate a simpler linear or quadratic function.
- A negative result simply means the curve dips below the x-axis more than it rises above it over that interval.
This calculator is provided for general educational and planning purposes.
Last reviewed August 2026