  We prove a conjecture of Denef on parameterized $p$-adic analytic integrals
using an analytic cell decomposition theorem, which we also prove in this
paper. This cell decomposition theorem describes piecewise the valuation of
analytic functions (and more generally of subanalytic functions), the pieces
being geometrically simple sets, called cells. We also classify subanalytic
sets up to subanalytic bijection.
