The longtime mayor of struggling Central Falls resigned and has agreed to plead guilty to a federal corruption charge of accepting gifts in exchange for handing out a lucrative contract to board up city houses, according to papers filed Wednesday. Charles Moreau, who resigned as mayor effective noon Wednesday, and his friend, businessman Michael Bouthillette, acknowledged in the plea agreement that Bouthillette paid at least in part for a furnace installed at Moreau’s former Central Falls home and for renovations at a house Moreau owned in Lincoln. The total value is estimated at $5,000 to $10,000. In exchange, Moreau used his emergency powers to order homes that were foreclosed be boarded up by Bouthillette’s business, prosecutors say.