Fourier transform of triangular pulse

Question

Triangular pulse

Calculations

I am having a hard time figuring out, how the above-highlighted integral is derived. Any hints would be great.

Answer 1

The highlighted integral is a change of variable, although they didn't change the letter used to represent the two variables. Try doing the substitution $u = -t$ and then replace the $u$ with $t$ once you're done, and you get the given result.