Limit and Linear Operator Interchange Question

Question

Let $X$ be Banach space. Let $f: (0, M) \ni s \mapsto f(s) \in X$ be continuous on $(0, M)$. Let $T:D(T) \subset X\to X$ be a linear closede operator.Then does the following holds?

$$ \lim_{\epsilon \to +0} T \int_\epsilon^M f(s)ds = T\int_0^M f(s)ds $$

if I assume that $\int_0^M \| f(s)\|ds < \infty$?