We perform new explicit and regularization-independent calculations of
< AV > amplitude in QED1+1 and < AVV > amplitude in QED1+3 respective
ly to reinvestigate the anomaly problem. A kind of finite and unambigu
ous terms of exact scale behavior (in momentum space) is found to be r
esponsible for the anomalies both in QED1+1 and QED1+3. They come from
logarithmically divergent momentum integrals in contrast with the usu
al knowledge for triangle anomaly in QED1+3. In QED1+1, this term is a
lso responsible for photon mass generation. Some implications and poss
ible relations with other aspects of anomaly are discussed.