suppose that f:R-->R is continuous. using the chain rule, or otherwise, show that the function F defined by

$\displaystyle F(x) = \exp(\int_0^xf)$ is differentiable and find its derivative.

Fundamental Theorem of calculus say that the derivative of $\displaystyle \int_a^xf(t)dt = f(x)$ I tried to use this to solve the above but no vain.

thanks for any help.