Global Frobenius theorem

See @lee2013smooth page 502, Theorem 19.21
Theorem (Global Frobenius Theorem). Let $D$ be an involutive distribution on a smooth manifold $M$. The collection of all maximal connected integral manifolds of $D$ forms a foliation of $M$.$◼$

It is worth noting that this result is one of the primary reasons why the notion of immersed manifold has been defined.