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We attempt to construct integral invariants with respect to supersymmetry in flat superspace. This problem can be translated into a homological problem of analyzing closed superforms. In this talk, we review the cohomology of superspace following Berkovits and Howe. We show that in flat superspace the cohomology groups appearing in their paper are related to the cohomology groups of the supersymmetry Lie algebra; one can calculate them using our previous results and the technique of spectral sequences. This talk is based on a joint paper with Michael Movshev and Albert Schwarz.