Lebesgue theorem says a bounded function $f$ is Riemann Integerable if and only if $f$ continuous almost everywhere.

Unfortunately, we know a function has antiderivative has no relation to Riemann Integerable.

$\textbf{Question}:$ Is there some nice equivalent condition of a real function has antiderivates?

Lebesgue theorem says that a bounded function $f$ is Riemann Integerable if and only if $f$ continuous almost everywhere.

Unfortunately, we know a function has antiderivative has no relation to Riemann Integerable.

Q. Is there some nice equivalent condition to the fact that a real function has antiderivates?