  We obtain a necessary and sufficient condition for the operator of
integration to be bounded on $H^\infty$ in a simply connected domain. The main
ingredient of the proof is a new result on uniform approximation of Bloch
functions. This gives a full characterization of symbols of certain Volterra
operators that act on bounded analytic functions in the disc if the symbol is
assumed to be univalent. Without this assumption the answer is not known, and
as the example at the end of the paper shows, the natural answer is definitely
false.
