this post was submitted on 02 Oct 2023
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It isn't that it doesn't matter, constant of integration is only used for indefinite integrals.
I think it's "indefinite" not "undefined" (at least in English).
The reason it doesn't matter/is only used for indefinite integrals is just that it gets subtracted out when you evaluate at the limits of integration, so it always goes away (but it's still there in the antiderivative).
(x1+c)-(x0+c) = x1-x0
You are correct, it has been at least ten years since my calculus classes which I took in a language that isn't English.