In our lecture we need to Fourier transform $\frac{\sin(x)^2}{x^2}$, i.e. compute the integral:
$$\int\_{-\infty}^{\infty} \mathrm e^{-iy x}\frac{\sin(x)^2}{x^2} \mathrm dx$$ 
Since it's a lecture on partial differential equations and not complex analysis, I don't think contour integration can be the solution here. I already tried to rewrite $\sin x$ getting 

$$\int\_{-\infty}^{\infty}\frac{-1}{4x^2} (\mathrm e^{ix(2-y)}-2\mathrm e^{-ixy}+\mathrm e^{-ix(y+2)})\mathrm dx$$

but now I'm still stuck with the computation of something like $$\int\_{-\infty}^{\infty}\frac{\mathrm e^{-ixy}}{x^2}\mathrm dx$$
Any ideas or hints are greatly appreciated. Thanks in advance!