  Let $X$ be a reduced complex space of pure dimension. We consider divergent
integrals of certain forms on $X$ that are singular along a subvariety defined
by the zero set of a holomorphic section of some holomorphic vector bundle $E
\rightarrow X$. Given a choice of Hermitian metric on $E$ we define a finite
part of the divergent integral. Our main result is an explicit formula for the
dependence on the choice of metric of the finite part.
