If $ f:I=[a,b] \subset \mathbb{R} \longrightarrow X$ is bounded by an integrable function so it is Bochner integrable?

Question

Let $X=(X,||\cdot||)$ be a Banach space and $f:I=[a,b] \subset \mathbb{R} \longrightarrow X$ a function such that $$ ||f(s)|| \leq g(s),\: \forall \: s \in I$$ for some $g:I \longrightarrow \mathbb{R} $ (Riemann) integrable.

With this I can conclude that $ f $ is Bochner integrable?