As it is well known, the notion of integrability of differential equations is not a uniform one, and different definitions are used within the frame of each theory. In this paper, the authors reconsider the classical integrability notion by quadratures, however without complementary assumptions like the existence of a symplectic structure etc. The integrability in the sense of Lie is generalized in order to be valid for more ample classes of systems. This perspective is actually motivated by the theory of distributions in the Frobenius sense, that is applied here to define the new notion of distributional integrability. As finite-dimensional Lie algebras correspond to a particular case of distributions, it turns out that the extrapolation to generic distributions allows to skip the usual assumption on the finite dimension of the underlying Lie algebra of vector fields. By means of certain algebraic constraints on the distribution, constants of the motion are successively obtained that allow to solve the system. This geometric formalism further allows to introduce local redefinitions of the time variable, however without violating the integrability properties. Besides being a novel and quite interesting approach to the integrability problem, the elegance of the formulation in this paper reminds of the geometric approaches to dynamics as developed by H. Weyl and E. Cartan.