I need help with the following problem.

Let $\displaystyle X$ be a continuous random variable with pdf $\displaystyle f(x)$ that is positive provided $\displaystyle 0<x<b<\infty$, and is equal to zero elsewhere. Show that

$\displaystyle E(X)= \int ^b _0 [1-F(x)]dx$ where $\displaystyle F(x)$ is the cdf of $\displaystyle X$.

Thanks in advance