Finding a density function.

A friend of mine was asking me for help with this exercise, and I'm not sure how to tackle it, could someone please help me.

a) We are given a density function for the random variables $\displaystyle Y_1$ and $\displaystyle Y_2$

$\displaystyle f(y_1 , y_2)=\begin{cases} e^{-y_1} &\quad\text{ if }\quad 0\leq y_2 \leq y_2 \leq \infty \\ 0 &\text{elsewhere}\end{cases}$

Now we are given a new random variable $\displaystyle U=Y_1 - Y_2$, and we need to find the density function for U.

b) Find $\displaystyle \mathbb{E}[U]$ and $\displaystyle \mathbb{V}[U]$

I could appreciate some help, I have not yet studied integrals in multiple variables, but I'm not sure if I have to do that for this problem.