  In the presence of back reaction, we first produce the one-loop corrections
for the event horizon and Hawking temperature of the Reissner-Nordstr\"om black
hole. Then, based on the covariant anomaly cancelation method and the effective
action technique, the modified expressions for the fluxes of gauge current and
energy momentum tensor, due to the effect of back reaction, are obtained. The
results are consistent with the Hawking fluxes of a (1+1)-dimensional blackbody
at the temperature with quantum corrections, thus confirming the robustness of
the covariant anomaly cancelation method and the effective action technique for
black holes with back reaction.
