one could conceive of a world where integrals are taught purely in terms of ... algebraic rules for manipulating integrals entirely in the realm of integrals wi

one could conceive of a world where integrals are taught purely in terms of ... algebraic rules for manipulating integrals entirely in the realm of integrals without relying on their pedagogical grounding in limits This is absolutely how I was first taught integral calculus. ∫x^n = x^{n+1}/(n+1) + C ∫e^x = e^x + C ∫(f+g) = ∫f + ∫g etc. Only later did I really learn the details of limits and the rigorous epsilon-delta underpinnings in real analysis. I used to think this was a bad thing, but now I’m not so sure. The word “calculus” does mean a system for calculation.