  The conformal anomaly and anomaly-induced effective action represent useful
and economic ways to describe semiclassical contributions to the action of
gravity. We discuss the anomaly in the case when the background is formed by
metric and scalar fields and formulate the induced action in two standard
covariant forms. The analysis of induced action at low energies reveals
existing connection to the renormalization group and effective potential. The
classification of anomalous terms is extended to the scalar background and
ambiguities in the total derivative terms in the anomaly are considered using
Pauli-Villars regularization.
