How to tell if a function is in $L^1$ or in $L^2$?

Question

Given a function, what properties do I need to satisfy to tell whether a function is in $L^{1}(R)$ and/or $L^{2}(R)$

For example, $\frac{sin(x)}{|x|^{\frac{3}{2}}}$.

Do I just need to test if the integrals/square integrals are finite?