I am having some trouble with antiderivatives. On occasion I see something like:

The antiderivative of f(x) $\displaystyle = \int_{0}^{x} f(x')dx'$

I don't understand why this is used since it isn't true for something as simple as f(x) = e^x, in which case it is off by a constant. Can someone let me know where my understanding has gone wrong and why this notation is used?