Steps of a Fourier transform

Hey everyone,

I'm stuck on a problem that requires me to show that the Fourier transform of f(t) is:

F(ω) = http://www4d.wolframalpha.com/Calcul...=49&w=251&h=36



given that f(t) = http://www4e.wolframalpha.com/Calcul...s=52&w=93&h=36 for |t|<1

Any help or intermediate steps or hints or anything of the sort would be massively appreciated!!

Sorry, not sure why the functions didn't come out. They were meant to be:
F(ω) = Attachment 24511

and given that f(t) = Attachment 24512