I have the following definition from Boothby:
"If $\Delta$ is a $C^\infty$ distribution on M and N is a connected $C^\infty$ submanifold of M such that for each $q\in N$ we have $T_q(N)\subset\Delta_q$, then we shall say that N is an integral manifold of $\Delta$."
Now if N is and integral manifold of $\Delta$ do I necessarily have that N is a submanifold of M?