Final answer:
The proofreading activity for bacterial DNA polymerase I is in the C-terminal domain, and for DNA polymerase III, it's within the epsilon subunit.
Step-by-step explanation:
The proofreading activity of bacterial DNA polymerase I resides in the C-terminal domain, and for DNA polymerase III, it's in the epsilon subunit. DNA polymerase I is a monomeric enzyme that, upon mild protease treatment, can be separated into a fragment that possesses the 5'→3' exonuclease activity and another large fragment called the Klenow fragment which has the polymerization and proofreading activity. DNA polymerase III on the other hand is an oligomeric protein composed of several subunits, among them the epsilon subunit crucial for proofreading.