I have calculated the FT of the rect function from -a to a and get this

\(\displaystyle \frac{\sin(2\pi k a )}{\pi k}\)

Now to perform the inverse

\(\displaystyle \int^\infty _{-\infty}\frac{\sin(2\pi k a )}{\pi k} e^{2\pi i k x} dk\)

I am not sure how to proceed from here, should I convert the sinc to and exponential?