  Considering arbitrary conformal field theories in general (non-conformally
flat) backgrounds, we adopt a dimensional regularization approach to obtain
stress tensors from Weyl anomalies. The results of type A anomaly-induced
stress tensors in four and six-dimensions generalize the previous results
calculated in a conformally flat background. On the other hand, regulators are
needed to have well-defined type B anomaly-induced stress tensors. We also
discuss ambiguities related to type D anomalies, Weyl invariants and order of
limit issues.
