Question

Switching bounds question.
How does one go from (2) to (3) on this page
http://www.claysturner.com/dsp/timereversal.pdf

Answer 1

they did a substitution

Answer 2

\[\int\limits_{-\infty}^{\infty} g(t) dt \\ \\ \int\limits^{t=\infty}_{t=-\infty} g(t) dt \\ \text{ let } t=-x \\ \text{ so } dt=-dx \\ \text{ and if } t=\infty \text{ then } -x=\infty \implies x=-\infty \\ \text{ and if } t=-\infty \text{ then } -x=-\infty \implies x=\infty \\ \text{ so you have } \\ \int\limits_{-\infty}^{\infty}g(t) dt= \int\limits_{\infty}^{-\infty} g(-x) (-dx) =-\int\limits_{\infty}^{-\infty} g(-x) dx\]