How can I find the Fourier Transform of a function given its time-plot using the Fourier Transform of another function?

Question

So I have $$X(Ω) = -j\frac{2π}{ω}δ(ω)$$

And I need to find the Fourier Transform of

and I need to find the Fourier transform of a square pulse $g(t) = 1 \text{ for } |t|<1.$

But I don't know where to start. I know how to get the Fourier Transform of the square pulse normally but no idea how to do it while using another Fourier Transform.