The theorem that establishes the connection between the two branches of calculus: differential calculus and integral calculus. The fundamental theorem of calculus is typically given in two parts. It says the following:

Suppose *f* is continuous on [a, b]. Then:

(1) The function

is an antiderivative of

*f,*i.e., g'(x) = f(x).

(2) (Evaluation Theorem) If F is an antiderivative of

*f,*i.e. F'(x) = f(x), thenThe two parts of the theorem can be rewritten like this:

(1)

(2)

**Important:**The theorem states that integration and differentiation are inverse operation. For the derivative of an integral of a function yields the original function, and the integral of a derivative also yields the function originally differentiated (up to a constant).

*credit: James StewartÂ©2013 www.PinoyBIX.com*