  We analyze the structure of the boundary terms in the conformal anomaly
integrated over a manifold with boundaries. We suggest that the anomalies of
type B, polynomial in the Weyl tensor, are accompanied with the respective
boundary terms of the Gibbons-Hawking type. Their form is dictated by the
requirement that they produce a variation which compensates the normal
derivatives of the metric variation on the boundary in order to have a
well-defined variational procedure. This suggestion agrees with recent findings
in four dimensions for free fields of various spin. We generalize this
consideration to six dimensions and derive explicitly the respective boundary
terms. We point out that the integrated conformal anomaly in odd dimensions is
non-vanishing due to the boundary terms. These terms are specified in three and
five dimensions.
