All work contracted for, unless done under Federal supervision, shall be done under the supervision of the district engineer. When the work is completed according to the contract, he shall make a detailed report of same to the directors, showing whether the contract has been fully complied with according to its terms, and if not, in what particular it has not been so complied with. The directors shall not be bound by such report, but may in addition thereto fully investigate such work and determine whether or not such contract has been complied with; and while such work is in progress, they shall inspect the same.