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 basical

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.