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The Federal Bureau of Investigation, often abbreviated to FBI, is a governmental organization. It is an agency of the United States Department of Justice that serves as both a federal criminal investigative body and an internal intelligence agency.
After Lisa's accusations about Bob Arnold accepting bribes, an FBI sting operation was put under way, watched from the F.B.I. Headquarters. The sting operation was successful in catching Arnold accepting a bribe and they arrested him.
Homer was sent undercover to Burns' manor by the FBI to find the 1 trillion dollar bill. However, Homer gets moved by a speech Mr. Burns makes and knocks out both Agent Miller and Agent Johnson and they run off.
They were investigating Fat Tony and asked Homer to go in undercover. He became known as Nicky Bluepants Altosaxophony and became close to Fat Tony. The FBI went in to arrest Tony when he had a heart attack after realizing that Nicky was a spy.