Let $f: \mathbb{R}\rightarrow{\mathbb{R}}$ be given by $f(x)=sen(\frac{1}{x})$ si $x\neq 0$ and $f(x)=c$ si $x=0$, where $c\in [-1,1]$ For which values of c there is an antiderivative?
Proof (attempt): I want to use a proposition: $f$ is continuous if, and only if, $osc(\Omega)=0$, because $f$ is discontinuous at all points $c\in [-1,1]$.