Let's say : $$\lim_{s\to 0} f(s) = C$$ Does the following limit of a Volterra integral holds?
\begin{equation} \lim_{T\to 0} \int_0^T f(s) K(s,T) ds = C \lim_{T \to 0} \int_0^T K(s,T)ds \end{equation}
Where $K(s,T)$ is well defined and finite.
Can anyone explain whether this relationship holds, if so, what is the "name" or lemma of this kind of relationship?