By the week of June 11, contractors are expected to sign off on the newly renovated academic wing and the newly constructed three-story science wing of the high school, according to town manager Wayne P. Marquis. There will be ample time to install furnishings and equipment, and other tasks needed to have the space ready for the opening of school in September, Marquis said. The milestone will mark the second for the $71 million project, which is being carried out by Bacon Construction Co., of Rhode Island. In January, the town accepted delivery of the renovated field house. This summer, contractors will turn their attention to demolishing the Dunn Wing, which has been serving as swing space during construction. They also will complete the renovation and expansion of the auditorium. Marquis said it is hoped the bulk of the demolition will be completed by the time the school year starts. The overall project, for which the Massachusetts School Building Authority is providing 57 percent reimbursement, is due to be completed in September 2013.