  Integral forms provide a natural and powerful tool for the construction of
supergravity actions. They are generalizations of usual differential forms and
are needed for a consistent theory of integration on supermanifolds. The group
geometrical approach to supergravity and its variational principle are
reformulated and clarified in this language. Central in our analysis is the
Poincare' dual of a bosonic manifold embedded into a supermanifold. Finally,
using integral forms we provide a proof of Gates' so-called "Ectoplasmic
Integration Theorem", relating superfield actions to component actions.
