1. Obtain from first principles, the Fourier transform of the function:

f(t) = 1, |t|<1 and 0, |t|>1

- I'm unsure of where to begin with this question, is it by using the formula (picture attached) and I don't know how to use the fact that |t|<1 or |t|>1

2. Find the fourier transform of

f(t) = u(t)e^(-at), a>0

- I know this can be read easily off tables but I tried using first principles and I found this statement (picture in red). A little off-topic but why is this statement true?

Any help would be greatly appreciated! Thanks in advance