fundamental theorem of calculus

Short definition from Wiktionary

Proper noun

1. 1
   A theorem of calculus consisting of two parts: For a continuous function f, an antiderivative or indefinite integral of F can be obtained as the integral of f over an interval with a variable upper bound, or: F(x)=∫ₐˣf(t),dt.
2. 2
   A theorem of calculus consisting of two parts: The definite integral of a continuous function f over a closed interval [a,,b] is equal to the net change of any antiderivative F over [a,,b], or: ∫ₐᵇf(x),dx=F(b)-F(a).