How did Polybos come to raise Oedipus as his own son?

After their marriage, King Laius of Thebes and his wife Jocasta were warned by the Delphic Oracle that should they have a son that son would kill Laius and marry Jocasta. It was not long after this warning that Jocasta gave birth to a son. Fearing the prophecy Laius pierced and bound the infant's feet and left him to die on a mountain side. A shepherd found the child and brought him to his king, King Polybius of Corinth. Polybus raised the child as his own, naming him Oedipus, which means "swollen-foot".