Integral

The accumulation of a function — the signed area under its graph between two points.

The definite integral ∫ₐᵇ f(x) dx is the signed area between the graph of f and the x-axis from a to b. The fundamental theorem of calculus links it to the antiderivative: ∫ₐᵇ f(x) dx = F(b) − F(a), where F'(x) = f(x).

∫ₐᵇ f(x) dx = F(b) − F(a)