  In recent years methods for the integration of Poisson manifolds and of Lie
algebroids have been proposed, the latter being usually presented as a
generalization of the former. In this note it is shown that the latter method
is actually related to (and may be derived from) a particular case of the
former if one regards dual of Lie algebroids as special Poisson manifolds. The
core of the proof is the fact, discussed in the second part of this note, that
coisotropic submanifolds of a (twisted) Poisson manifold are in one-to-one
correspondence with possibly singular Lagrangian subgroupoids of
source-simply-connected (twisted) symplectic groupoids.
