  We give a pedagogical introduction to integration techniques appropriate for
non-commutative spaces while presenting some new results as well. A rather
detailed discussion outlines the motivation for adopting the Hopf algebra
language. We then present some trace formulas for the integral on Hopf algebras
and show how to treat the $\int 1=0$ case. We extend the discussion to braided
Hopf algebras relying on diagrammatic techniques. The use of the general
formulas is illustrated by explicitly worked out examples.
