  We present a study on the integral forms and their Cech/de Rham cohomology.
We analyze the problem from a general perspective of sheaf theory and we
explore examples in superprojective manifolds. Integral forms are fundamental
in the theory of integration in supermanifolds. One can define the integral
forms introducing a new sheaf containing, among other objects, the new basic
forms delta(dtheta) where the symbol delta has the usual formal properties of
Dirac's delta distribution and acts on functions and forms as a Dirac measure.
They satisfy in addition some new relations on the sheaf. It turns out that the
enlarged sheaf of integral and "ordinary" superforms contains also forms of
"negative degree" and, moreover, due to the additional relations introduced,
its cohomology is, in a non trivial way, different from the usual superform
cohomology.
