Fundamental theorem of calculus

The fundamental theorem of calculus is a theorem that links the concept of the derivative of a function with the concept of the function's integral.

The first part of the theorem, sometimes called the first fundamental theorem of calculus, is that the definite integration of a function is related to its antiderivative, and can be reversed by differentiation. This part of the theorem is also important because it guarantees the existence of antiderivatives for continuous functions.