What is the difference between an indefinite integral and an antiderivative? I thought these were different words for the same thing, but it seems I am wrong. Help.

An anti-derivative of a function $f$ is a function $F$ such that $F'=f$.
The indefinte integral $\int f(x)\,\mathrm dx$ of $f$ (that is, a function $F$ such that $\int_a^bf(x)\,\mathrm dx=F(b)-F(a)$ for all $a<b$) is an antiderivative if $f$ is continuous, but need not be an antiderivative in the general case.
