I'm pretty sure we did proofs in high school. But that was a while ago, don't know what they do now.

Hey now that I think of it, "mathematical analysis" had continuity, limits, some integrals. And then every mathematically inclined uni specialization had "integral and differential calculations (let's shorten it to calculus)" which was more advanced use of integrals :)

A rose by any other name would smell as sweet, but it may be called a thorn in a different locale.