Let $X_M^c$ be the space of vector fields on a manifold $M$ with compact support. Prove that $X_M^c=[X_M^c,X_M^c]$

Question

Let $X_M^c$ be the space of vector fields on a manifold $M$ with compact support. Prove that $X_M^c=[X_M^c,X_M^c]$.

Proving that $[X_M^c,X_M^c]\subset X_M^c$ is relatively simple. However, I have not been able to prove $X_M^c\subset [X_M^c,X_M^c]$. Any clues?