The fundamental theorem of calculus establishes a connection between differentiation and integration, demonstrating that they are inverse operations. The theorem has two parts:

If is an antiderivative of a continuous function on the interval , then the definite integral of over that interval is given by:

If is a continuous function on an interval containing , and is an antiderivative of on that interval, then the derivative of the integral of with respect to is equal to the original function: