TITLE: Multiple antiderivatives?
QUESTION [5 upvotes]: The way I have seen the fundamental theorem of calculus stated is:
$$\int_a^bf(x)\ dx=F(b)-F(a)$$
Where $F(x)$ is any antiderivative of $f(x)$. Does the "any antiderivative" refer to the constant $C$ that is always added to the integral, or are there functions that have several completely different antiderivatives?

REPLY [5 votes]: Yes, your first hunch is right. "Any" antiderivative refers to the fact that an antiderivate is really a family of functions which differ only by a constant.