"'After an absence of several years, I came to Jerusalem to bring my people gifts for the poor and to present offerings. I was ceremonially clean when they found me in the temple courts doing this. There was no crowd with me, nor was I involved in any disturbance.'" NIV translation
Now, Paul directly confronts the false charges. He points out that he was in complete agreement with the law (ceremonially clean) and was going to present offerings. He also adds that there was no crowd or disturbance.
"'But there are some Jews from the province of Asia, who ought to be here before you and bring charges if they have anything against me.'" NIV translation
He continues to explain that, if anyone had a reason to present the charges it would be some Jews from Asia where he had done most of his work. They were not there in front of Felix just as they were not present before the Sanhedrin.
"Or these who are here should state what crime they found in me when I stood before the Sanhedrin - unless it was this one thing I shouted as I stood in their presence: 'It is concerning the resurrection of the dead that I am on trial before you today.'" NIV translation
Paul continues by sharing the fact that he was not found guilty of any crime when he was brought before the Sanhedrin. Then, he gives the real reason that he was put on trial again and that was because he preached the message of the resurrection.
"Then Felix, who was well acquainted with the Way, adjourned the proceedings. 'When Lysias the commander comes,' he said, 'I will decide your case.' He ordered the centurion to keep Paul under guard but to give him some freedom and permit his friends to care of his needs." NIV translation
So, after hearing both sides, Felix, whose name means "pleasure" and who was a cruel and immoral man, decides not to decide. He puts the decision off and holds Paul but gives him more freedoms than normal. Felix new about the Jewish laws and even he could see that Paul was not guilty but he still did not release him. We might ask why God would let His child suffer under arrest like that and the simple answer is that we see parts but God sees His whole plan and He knows what is truly best.
"Several days later Felix came with his wife Drusilla, who was a Jewess. He sent for Paul and listened to him as he spoke about faith in Christ Jesus." NIV translation
Now, we see why God would allow this to happen and we see this immoral man about to hear the gospel of Jesus Christ. This man was a politician and so would not have done the right thing unless there was something in it for himself. He came expecting a bribe but instead got a lesson on the coming judgment.