I am trying to evaluate:
$$I = \int_{-\infty}^{\infty} \frac{\sin^2(x)}{x^2} \, dx.$$
Using a contour semi-circle (upper plane), I can get:
$$ \oint_{C} f(z) \,dz = \oint_{C} \frac{1 - e^{2iz}}{z^2} \, dz.$$
The whole issue is the $z^2$. I cannot use the residue theory, because it lies *on* the contour.

**I don’t want a full solution.** I really want to try on my own, I just need some guidance!