> You don't need to think about periodic functions at all.
except you just described that which is called period...so it's actually good for a student to notice these things, and use the correct term, so that they can associate the name with the idea.
I don't think many would notice doing it that way, as it's disguised by the different limits and constant factors. The indefinite integrals are what is basically the same on the surface. There's more to periodicity than different sections being similar on the surface, and there's certainly no need for them to use the correct terms.
> You don't need to think about periodic functions at all.
except you just described that which is called period...so it's actually good for a student to notice these things, and use the correct term, so that they can associate the name with the idea.