“He hoped also that money should have been given him of Paul, that he might loose him: wherefore he sent for him the oftener, and communed with him.”
Acts 24:26

Maybe Paul knew what Felix’s intentions were, maybe he didn’t, but one thing was certain with Paul- when granted audience; he preached the gospel.
The more Felix called him expecting a bribe, the more Paul emphasized faith in Christ:
“…Felix came with his wife Drusilla, which was a Jewess, he sent for Paul, and heard him concerning the faith in Christ. And as he reasoned of righteousness, temperance, and judgment to come…” Acts 24:24-25
And how compelling he must have been because the Bible tells us:
“…Felix trembled, and answered, Go thy way for this time; when I have a convenient season, I will call for thee.” Acts 24:24-25
Thank God he focused on the gospel not minding the designation of Felix, because how can one reason of righteousness, self control and judgement and still go ahead and give bribes?
“For if I build again the things which I destroyed, I make myself a transgressor.” Galatians 2:18
The preaching of the gospel will guard you against walking in unrighteousness.

Bible Reading Plan: Psalms 16 and Joshua 2