probability - Expectation of nonnegative Random Variable

Can someone help me give me some pointers as to how to prove this relation?

Answer

Let p be the probability measure. We have that $\int_{0}^{\infty}\left[1-F\left(x\right)\right]dx=\int_{0}^{\infty}\Pr\left[X>x\right]dx=\int_{0}^{\infty}\left[\int1_{X>x}dp\right]dx $ using Fubini's theorem we have $\int_{0}^{\infty}\left[\int1_{X>x}dp\right]dx=\int\left[\int_{0}^{\infty}1_{X>x}dx\right]dp=\int Xdp=E\left[X\right] $