Classically conformal invariance implies that the energy-momentum tensor is traceless. At the quantum level tracelessness is generally violated by renormalization group effects but also, importantly, by terms of geometrical origin. However, the latter must satisfy suitable integrability conditions a la Wess-Zumino. I want to discuss how to obtain such integrable terms in a model-independent way using a curved space generalization of the embedding formalism of conformal field theory known as ambient space. As a byproduct, I will also discuss how to actually integrate the anomaly in the form of nonlocal effective actions previously discussed in the literature but also highlight some limitations of this approach.