If we get to use calculus, I'd evaluate this:

\(\displaystyle \int_{-\infty}^{\infty} y\cdot f_{Y}

\;dy\)

Of course, I would also check for validity by verifying:

\(\displaystyle \int_{-\infty}^{\infty} f_{Y}

\;dy\) = 1

Without the calculus, the geometry is not difficult.

\(\displaystyle \frac{1}{2}\cdot\frac{3}{4} + \frac{5}{2}\cdot\frac{1}{4}\)

Unique answers don't care how you find them.