  In this paper we extend the Lie theory of integration in two different ways.
First we consider a finite dimensional Lie algebra of vector fields and discuss
the most general conditions under which the integral curves of one of the
fields can be obtained by quadratures in a prescribed way. It turns out that
the conditions can be expressed in a purely algebraic way. In a second step we
generalize the construction to the case in which we substitute the Lie algebra
of vector fields by a module (generalized distribution). We obtain much larger
class of integrable systems replacing standard concepts of solvable (or
nilpotent) Lie algebra with distributional solvability (nilpotency).
