/sci/ - Science & Math

I'm doing integrals, when doing definite integrals, the general statement is [math]\int^b_af(x)dx=F(b)-F(a)[/math]. This is saying that you're supposed to evaluate an integral from whatever arbitrary point to b minus integral evaluated from that same arbitrary point to a, and that difference would give the area you're looking for, ie a to b.

Now what I don't understand is this arbitrary point part: like if you're able to just choose some arbitrary starting point and evaluate the integral from that point to b, why couldn't you simply just choose that arbitrary point to be a in the first place, so instead of going around the problem, taking the difference of areas from some arbitrary fucking point to b and that same point to a, why not just make the arbitrary point a, evaluate at b and here's the area?

I just started studying this and I'm clearly missing something because this "workaround" makes no sense.