Definite+Integrals+Fundamental+Theorem+of+Calculus+Parts+I+and+II

he first Fundamental Theorem of Calculus says that the definite integral of a continuous function is a differentiable function of its upper limit of integration.

If f is continuous on [a,b], then the function: has a derivative at every point x in [a,b], and

The second Fundamental Theorem of Calculus says that the definite integral of a continuous function from a to b can be found from any one of the function;s antiderivates F as the number F(b)-F(a).

If f is continuous at every point of [a,b], and if f is any antiderivate of f on [a,b], then This is also known as the Integral Evaluation Theorem