# How to get bounds of integration after transformation?

I came across the answer to this question, how to calculate mean and variance for logistic distribution but can't figure out or understand how the bounds switched from ($-\infty$, $\infty$) to (0,1) on the first answer. I haven't studied calculus in a very longtime so I've forgotten quite a bit and just can't figure this out even after consulting a few text books. Can someone provide some instruction on how the revised bounds are found after transforming from $y$ to $z$ in the answer? I don't have a high enough reputation to post a comment under the original answer; otherwise, I would have.

Thank you!