We show that a cellular complex described by Floege allows to determine the integral homology of the Bianchi groups $PSL_2(O_{-m})$, where $O_{-m}$ is the ring of integers of an imaginary quadratic number field $\rationals[\sqrt{-m}]$ for a square-free natural number $m$. We use this to compute the integral homology in the cases m = 5, 6, 10, 13 and 15, which before was known only in the Euclidean cases m = 1, 2, 3, 7 and 11.