definite integral

The definite integral of a function $f$ on an interval $[a, b]$ is the signed area bounded by $f$ and the $x$ -axis.

Formally,

S = {(x, y) : a \leq x \leq b, 0 < y < f (x)} = \int_{a}^{b} f (x) d x

The definite integral can be computed via the antiderivative through the Fundamental Theorem of Calculus.