My math teacher and I got in a debate the other day, and i couldn't find any information anywhere so i figured i'd post it here
We were working on calculating infinite converging areas and we got to the following problem
Since i'm always looking for ways to avoid doing extra work, i said it would be possible to simply cancel out the areas from 1 to 0 and from 0 to 1 based on symetry and end up with zero
however, when you actually work out the integral you get

which is undefined
As far as i can tell, the reason that is undefined is because the two infinities could be coming from anywhere and it's impossible to make an assumption, but in this case, when we know the two infinite areas are exactly equal (except for the minus sign) why can't we say that is equal to zero?