  In this paper, we introduce an algorithm for computing p-adic integrals on
bad reduction hyperelliptic curves. For bad reduction curves, there are two
notions of p-adic integration: Berkovich-Coleman integrals which can be
performed locally; and abelian integrals with desirable number-theoretic
properties. By covering a bad reduction hyperelliptic curve by annuli and basic
wide open sets, we reduce the computation of Berkovich-Coleman integrals to the
known algorithms on good reduction hyperelliptic curves. These are due to
Balakrishnan, Bradshaw, and Kedlaya, and to Balakrishnan and Besser for regular
and meromorphic 1-forms on good reduction curves, respectively. We then employ
tropical geometric techniques due to the first-named author with Rabinoff and
Zureick-Brown to convert the Berkovich-Coleman integrals into abelian
integrals. We provide examples of our algorithm, verifying that certain abelian
integrals between torsion points vanish.
