[SOLVED] question on expectations and cumulative distribution functions

I want to prove that is true with the only information given being that X is a continuous RV such that P(X > 0) = 1.

The hint that I've received from my teacher is to replace with the integral of the pdf, to get (using dummy variable t) and then switch the order I do the integrals.

Also, with (the definition of E(X)) I'm not sure how I would integrate this without knowing exactly what f(x) is.

Thanks in advance for any help :)