Complex sentence: The sports teams all participate in the NCAA's Division I and as of July 1,2013, the Owls will be primary members of the American Athletic Conference after spending the previous 31 years in the Atlantic Ten Conference (A- 10).
Split into simpler sentences: The sports teams all participate in the NCAA's Division I and the American Athletic Conference (The American). The Owls moved after spending the previous 31 years in the Atlantic Ten Conference (A- 10).