  We present a general, functorial approach to Motivic Integration for
separated schemes of finite type in lieu of recent work by Hans Schoutens on
the subject. Presented is a change of variables formula and a hierarchy of
stability properties which are closely connected to the integrability of
Motivic functions for schemes. Most notably, we prove that if a scheme has
smooth reduction then it has a natural geometric definition of motivic volume
in the Grothendick ring of the formal motivic site.
