LONDON — Arsene Wenger’s turbulent year ended with a third FA Cup success in four seasons after Arsenal beat Chelsea 2-1 to deny the English Premier League champion a double on Saturday. Wenger became the competition’s most successful manager with a seventh title in his 21-year reign, triumphs that have papered over some of the cracks as Arsenal has repeatedly come up short in the Premier League and Champions League. Just as the season reached its climax at Wembley Stadium, Arsenal turned in the type of tenacious display lacking so often, and against a side so commanding in the Premier League.