Abstract: Eisenstein series arise from parabolic inductions of cuspidal representations of the Levi subgroup of the Siegel parabolic subgroup of GSp_4 contribute to the degree 1 coherent cohomology of automorphic vector bundles on Siegel 3-folds. Their constant terms involve special values of the standard L-function for GL_2, which may be used to study related arithmetic problems. However, the absence of a q-expansion principle in higher degrees limits the study of their integrality. In this talk, we give a construction of explicit families of these Eisenstein cohomology classes that are integral within the framework of higher Hida theory, and explain the key points that ensure their integrality.