My teacher marks it wrong when I include it on definite integrals, but I was taught to always add it. What's the actual rule?
Accepted answer
Only **indefinite** integrals need `+ C`. An indefinite integral represents an entire family of antiderivatives, so the constant is part of the answer.
A definite integral evaluates to a single number, and the constant cancels:
∫ₐᵇ f(x)dx = [F(b) + C] − [F(a) + C] = F(b) − F(a)
So writing `+ C` on a definite integral isn't just unnecessary, it signals you're treating a number as a family of functions. Keep `+ C` for `∫f(x)dx` and drop it the moment you apply limits.