Fourier transform of x(t)=u(t)-u(t-1)

[mugzieee]

Im trying to get the Fourier transform of x(t)=u(t)-u(t-1)
from what i know the FT of u(t) is pi*delta(omega)+1/jw
so for the u(t-1) would we have to use the time shifting property of Fourier transforms so that it becomes pi*delta(omega)+1/jw*(exp(-jw_o)??

 

[doodle]

A small correction:
$$[\pi\delta(w) + 1/(jw)] e^{-jw} = \pi\delta(w) + e^{-jw}/(jw)$$