The fundamental theorem of calculus is a theorem that links the concept of differentiating a function with the concept of integrating a function.
The first part of the theorem, sometimes called the first fundamental theorem of calculus, states that one of the antiderivatives (also called indefinite integral), say F, of some function f may be obtained as the integral of f with a variable bound of integration. This implies the existence of antiderivatives for continuous functions.
Conversely, the second part of the theorem, sometimes called the second fundamental theorem of calculus, states that...