Interchange of limits in integrals

[iocal]

Hi guys, I would like to ask under what conditions you can interchange the limits of an integral and multiply the integral by (-1).
From what I understand it has to be a continuous function, is that right? Can you do it in the following integral for example?

\(\displaystyle \displaystyle -\int_0^{\infty} y\ f(c+y)\ dy = \int_{-\infty}^0 y\ f(c+y)\ dy\)

Does the equality hold?
Thanks in advance.

 

[HallsofIvy]

As long as the function, f, is integrable, is true that \(\displaystyle \int_a^b f(x)dx= -\int_b^a f(x)dx\). Of course, if f is NOT integrable, neither \(\displaystyle \int_a^b f(x)dx\) nor \(\displaystyle \int_b^a f(x)dx\) is defined!