Suggest me how should I solve this using Parseval's identity:
$\int_{-\infty}^{\infty} \frac{\sin(at)\sin(bt)}{(a^2+t^2)(b^2+t^2)} dx=2a$(when $a<b$) and $=2b$(when a>b) with $a>0$ and $b>0$
Parseval's Identity:If $\mathscr{F}${$f(t)$}= $F(s)$ and $\mathscr{F}${$g(t)$}= $G(s)$ then
$\int_{-\infty}^{\infty}f(t)\bar{g}(t)dt=\int_{-\infty}^{\infty}F(s)\bar{G}(s)$ and
$\int_{-\infty}^{\infty}|f(t)|^2= \int_{-\infty}^{\infty}|F(s)|^2$
Please give me hint how should I solve this problem.What should I choose f(t) and g(t) as? Thanks in advance!