How to show $\int_{1}^{\infty} \frac{\sin^2(x)}{x^2}dx$ is finite? At first, my approach was to directly take the improper integral of it. 
However, it seems not that easy.
Then I tried to find another fraction to make a comparison. I got $\frac{\sin^2(x)}{x^2} < \frac{\sin^2(x)}{x}$. So if I could show $\int_{1}^{\infty} \frac{\sin^2(x)}{x}dx $ is finite，$\int_{1}^{\infty} \frac{\sin^2(x)}{x^2}dx$ will then be finite . Nevertheless, I still cannot figure the latter out.
Could anyone suggest me what function to compare to, or other method?
Thank you!

Hint: compare with the integral $1/x^2$
