The transform is simple, but I am sure I am missing something in the end.

f(t) =

0 for [-inf --> 2]

8 for [2 --> 6]

0 for [6 --> +inf]

If i just put a standart Fourier transform equation into it and put limits for integral as 2 (for lower) and 6 (for higher) I come up with two e^-j terms in the end and I cant use any of the euler's equations 'Relationship to trigonometry' (wiki reference) quations to simplify it.

I was thinking to shift rect function in time so i would have -2 and 2 as for integral limits, that would help, or if i could make one of the terms disappear by putting integral limits as 0 and 4.