Say you want to write (where is an antiderivative of )
for the odd 2-periodic function
then would G(x) be
You couldn't just write
If you look at the antidervative of g over a given interval (say -1,0), then you have g(t)=-10, which has -10x as an antiderivative
So over this interval,
So no you can't write the last part you did. It would be like you integrate from 0 to x, which is false !
It's easy to see that on a graph, since the integral is the area under the line at y=-10
I don't know if it's clear... ?