calculus - Integral $intfrac{(sin(x))^2}{x^2+1} dx$

I have no idea of variable changement to use or other to calculate this integral :

$$\int_0^{\infty}\frac{(\sin(x))^2}{x^2+1}\,dx$$

Wolfram alpha gives me the result but really no idea ...

I seek a calculus without residues theorem or other big theorems like it because I didn't learn them.. so just by part or by variable changement if possible sure..

Thanks in advance,

Shadock