Integrals and integration   Integration is a process by which
local data over a manifold or similar is accumulated to an
integral.  In its simplest form, this is a limiting notion of
the process of forming sums, known then as Riemann integration
or Lebesgue integration, where the integration pairs a function
on a space against a measure which indicates, roughly, how much
a local contribution of the function contributes to the whole
accumulation process. Direct variants and refinements of this
kind of integration is integration of differential forms and
similar.  The integration of differential forms induces a more
general notion of integration, namely integration in
differential cohomology and hence integration in generalized
cohomology. Here the choice of a measure is replaced by a choice
of orientation in generalized cohomology.  analytic
integrationcohomological integration measureorientation in
generalized cohomology Lebesgue integration, of differential
formspush-forward in generalized cohomology/in diff