Find with proof the following limit:
$$\lim_{n \to \infty} \int_{-\infty}^{\infty} \frac{(\sin(x))^n}{x^2}dx$$
I want to use the DCT but I cannot seem to dominate $f_{n}(x)=\frac{(\sin(x))^n}{x^2}$ by an integrable function. Any help would be appreciated.