The Salt Lake Tribune (Sunnie Redhouse) reports: After a month of the NBA summer league, Jaycee Carroll has decided to play professional basketball in Italy. The Utah State graduate signed a one-year contract to play with Siviglia Wear Teramo, an A1 Italian professional basketball team. He will report to the team on Aug. 25.    Carroll said the decision came after many conversations with his agent and basketball organizations. “We were looking at every option that we had,” Carroll said. “We were thinking that an NBA team was going to make an offer.” But none did. Nothing solid anyway.