Abstract: The study of integrals is an important topic in the theory of Hopf algebras. This notion was introduced by Sweedler in 1969 motivated by the uniquenness of the Haar integral on locally compact groups. In this talk we focus on the representation theory of integrals and explain how special types of integrals can produce (Anti)-Yetter-Drinfeld modules. This can be used to classify total integrals and (cleft) Hopf Galois extensions.