The operad of moulds is realized in terms of an operational calculus of
formal integrals (continuous formal power series). This leads to many
simplifications and to the discovery of various suboperads. In particular, we
prove a conjecture of the first author about the inverse image of non-crossing
trees in the dendriform operad. Finally, we explain a connection with the
formalism of noncommutative symmetric functions.Comment: 16 pages, one reference added and minor changes in v
