On N=1 exact superpotentials from U(N) matrix models

In this letter we compute the exact effective superpotential of N = 1 U(N) supersymmetric gauge theories with Nf fundamental flavors and an arbitrary tree-level polynomial superpotential for the adjoint Higgs field. We use the matrix model approach in the maximally confining phase. When restricted to the case of a tree-level even polynomial superpotential, our computation reproduces the known result of the SU(N) theory.