Let π be a discrete group. We shall introduce the more general concept of an integral of a weak Doi-Hopf π-datum (H, A, C), where H is a weak Hopf π-coalgebra coacting on an algebra A and acting on a π-coalgebra C = {Cα}α∈π. We prove that there exists a total integral θ = {θα : Cα → Hom(Cα−1 , A)}α∈π, then any representation of (H, A, C) is injective in a functorial way, as a corepresentation of C and vice versa. As the application of the existence of a total integral, we prove the Maschke-type Theorem for weak Doi-Hopf π-modules.