  The Coleman integral is a $p$-adic line integral that plays a key role in
computing several important invariants in arithmetic geometry. We give an
algorithm for explicit Coleman integration on curves, using the algorithms of
the second author to compute the action of Frobenius on $p$-adic cohomology. We
present a collection of examples computed with our implementation. This
includes integrals on a genus 55 curve, where other methods do not currently
seem practical.
