Is there a formal definition for antiderivatives?
In the way the derivative can be defined as a limit, specifically
or any of the other possible variants, is there a way to define the antiderivative, as in indefinite integral?
The handful of sources I've looked over (Wikipedia and MathWorld, to name a few) all refer to the antiderivative simply as a "nonunique inverse operator" (I'm paraphrasing). I can't say I'm completely satisfied with this notion. Is the following the best we can do?
If F(x) is a function that satisfies , then F(x) is called an antiderivative of f(x). (Forgive the lack of formality.)