We study the connectedness property of the spectrum of forcing algebras over a noetherian ring.In particular we present for an integral base ring a geometric criterion for connectedness in terms of horizontal and vertical components of the forcing algebra.This criterion allows further simplifications when the base ring is local, or one-dimensional, or factorial.Besides, we discuss whether the connectedness of forcing algebras is a local property.Finally, we present a characterization of the integral closure of an ideal by means of the universal connectedness of the corresponding forcing morphism.