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I think that at that point calculus was a grad-school-level thing. At the very least, it wasn't being taught in high schools. In fact, I'm pretty sure it's only taught in high schools today under the aegis of Advanced Placement classes, which give you college credit.

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Many, many schools today offer "College Prep" calculus, which is far less rigorous than AP Calc. It covers most of the same topics, but with less depth. It's unlikely a College Prep Calc class would spend much time, if any, memorizing Trig Identities for integration. Generally very little epsilon-delta work, etc.

I'd be surprised if they do more than mention that epsilon-delta stuff exists. Most AP calc classes have very little epsilon-delta work. We spent maybe two or three days on it in mine, certainly not enough time to write a full proof, and that was more than most people I've talked to who did it at different high schools. If my experience is at all representative, that rigorous of a development of calculus isn't normal until upper-level classes, when you're heading towards analysis.

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