Expected value of $\sin(x)$ I have a uniformly distributed random variable $ \omega $ in the range $[\frac\pi2, \frac\pi{-2}]$. Then I have the function $ s = \sin(\omega) $  I want to calculate the expected value of this function $ s $. 
So far I know that the uniformly distributed random variable can be written as $$ \omega = \frac1{\frac\pi2 - - \frac\pi2} = \frac 1\pi $$
Then I don't know if the correct way of calculating the expected value is $$ E = \int_{-\frac\pi2}^{\frac\pi2} \frac1\pi \sin(x) dx $$
or if I'm completely off. 

Your working seems fine. 
And by the fact that sine is an odd function and $\omega$ is uniformly distributed symmetrically about $0$, the integral is evaluated to be $0$.
