  Vologodsky's theory of $p$-adic integration plays a central role in computing
several interesting invariants in arithmetic geometry. In contrast with the
theory developed by Coleman, it has the advantage of being insensitive to the
reduction type at $p$. Building on recent work of Besser and Zerbes, we
describe an algorithm for computing Vologodsky integrals on bad reduction
hyperelliptic curves. This extends previous joint work with Katz to all
meromorphic differential forms. We illustrate our algorithm with numerical
examples computed in Sage.
