We introduce the notion of variational bihamiltonian cohomology to study properties of a class of integrable evolutionary PDEs, which are associated to semisimple Frobenius manifolds and have close relations with the study of 2d topological field theory and the Gromov-Witten theory. We show the existence of Virasoro symmetries of such integrable systems by computing the associated variational bihamiltonian cohomology groups, and prove the polynomiality property of their bihamiltonian structures.