Swapping the limits of integration

[Pythagorean]

Can you always just swap the limits of integration and flip the sign of a one-dimensional integral or is there a time when you can't do this?

 

[HallsofIvy]

Yes, $\int_a^b f(x) dx= -\int_b^a f(x) dx$. Let u= -x. I thought everyone knew this!

 

[Pythagorean]

Yes, $\int_a^b f(x) dx= -\int_b^a f(x) dx$. Let u= -x. I thought everyone knew this!

I was taught that yes... but it's not too uncommon to be taught something that's a special case without being told it's a special case.

The question came from the fact that in electromagnetism, we define the potential by the negative of the integral with swapped limits. I'm not sure why you would put the extra step in there if there wasn't a case where the positive with the limits restored wouldn't be equivalent.

My assumption (given your response) is that they do it simply because we generally define potential from some point at infinity down to a local point.