So the first part of the questions asks us to find the Fourier Transform of $$ f(x) = \left\{ \begin{array}{ll} e^{y} & \quad {-\infty}<x < 0 \\ e^{-y} & \quad 0<x < {\infty} \\ \end{array} \right. $$ which is $$ \frac{2}{1+k^2}$$
then it says work out the Fourier Transform of $$ g(x) = \left\{ \begin{array}{ll} 1 & \quad |x| \leq 2\pi\ \\ 0 & \quad \text{otherwise} \end{array} \right. $$
which is
$$ \frac{2\sin(2k\pi)}{k}$$
The final part says calculate the integral of
$$\int_{-\infty}^{+\infty} \left|{\frac{\sin{x}}{x(1+x^2)}}\right|^2\,dx $$
Now, I think I probably first have to use the convolution theorem to calculate $h(x)=f(x)\cdot g(x)$ then use Parseval's Theorem to get the integral but for some reason it doesn't seem to give a convergent answer? Can someone please help explain how I get it to converge?