  We give a completely explicit upper bound for integral points on (standard)
affine models of hyperelliptic curves, provided we know at least one rational
point and a Mordell-Weil basis of the Jacobian. We also explain a powerful
refinement of the Mordell--Weil sieve which, combined with the upper bound, is
capable of determining all the integral points. Our method is illustrated by
determining the integral points on a two genus 2 hyperelliptic curves with
Mordell--Weil Jacobian ranks of 3 and 6.
