Compactly supported smooth sections dense in the space of $L^{2}$-sections?

Let $(M,g)$ be a complete Riemannian manifold (not necessarily compact) and $E$ be a finite-rank vector bundle equipped with some positive-definite bundle metric $\langle\cdot,\cdot\rangle_{E}$. Then, we can define the space of $L^{2}$-sections w.r.t. to the natural $L^{2}$-inner product$$\langle s,t\rangle_{L^{2}}:=\int_{M}\langle s,t\rangle_{E}\,\mathrm{vol}_{g}$$

Is the space $\Gamma^{\infty}_{c}(E)$ dense in $L^{2}(E)$?

I was trying to find a reference for this in the interenet, but I was not able to find any.