Dense subspaces of the space $L^p(0,T;X)$

Question

Given a Banach space $X$ and $1\leq p<\infty$, let's define the space $L^p(0,T;X)$ as the set of all strongly measurable functions $f:(0,T)\mapsto X$ such that $$\int_0^T\Vert f\Vert_{X}^pdt<\infty$$ (with the usual modifications when $p=\infty$). I'm looking for dense subspaces of $L^p(0,T;X)$; for instance, we konw that for usual Lebesgue space $C_0^\infty$ is dense in $L^p$. Are there similar results for the space $L^p(0,T;X)$? In particular I would like to regularize a function in $L^p(0,T;X)$ in time.