Distribution integrable in one point implies integrable in neighborhood? – mathoverflow.net

Let $M$ be a smooth manifold. Let $D\leq TM$ be a subbundle i.e. a distribution of rank $k$. Then $D$ is integrable at $p \in M$ if there is a submanifold $N \subseteq M$ with $p \in N$ and $T_xN = ...