Let C be a curve of genus 2 defined over a number field, and Θ \Theta the image of C embedded into its Jacobian J. We show that the heights of points of J which are integral with respect to [ 2 ] ∗ Θ {[2]_\ast }\Theta can be effectively bounded. As a result, if P is a point on C, and P ¯ \bar P its image under the hyperelliptic involution, then the heights of points on C which are integral with respect to P and P ¯ \bar P can be effectively bounded, in such a way that we can isolate the dependence on P, and show that if the height of P is bigger than some bound, then there are no points which are S-integral with respect to P and P ¯ \bar P . We relate points on C which are integral with respect to P to points on J which are integral with respect to Θ \Theta , and discuss approaches toward bounding the heights of the latter.