Given a function defined on interval .Provethat there must exist a function with the property that .

With this we can prove the second fundamental theorem of calculus. We have to show that if then . Instead of the classical proof with a Riemann Sum we may do the following: Since by the first fundamental theorem of calculus, "If there exists an anti-derivative of then " But by the existence of anti-derivative conjecture there MUST exist such a function thus, but then because is a constant-function.