I want to prove the following statement.
If $f$ is uniformly continuous on the open interval $(a, b)$, then $f$ is an indefinite integral of some $g\in R(a, b)$.
The answer says that this statement is true, and I want to prove it. However, I don't know the sufficient and necessary conditions that would make some function an indefinite integral of some other function. If $f$ is differentiable, then taking $g(x)=\frac{d}{dx}f(x)$ would make it an indefinite integral of some other function, but uniformly continuous does not imply differentiable. How would I do this?