The use of unsteady incompressible-flow simulations has become very popular for aeroacoustic noise predictions at low Mach numbers, as it provides a good compromise between computational time and reliable predictions. The acoustic radiation of the aerodynamic sources is calculated in a second step by solving an appropriate system of acoustic equations. In order to predict the noise produced by confined flows, two integral formulations of Lighthill-Curle's analogy are developed. Both formulations require only the knowledge of the incompressible-flow pressure. The first one, which is based on Ribner's reformulation of Lighthill's source terms, is exact and shall serve as a reference to the second approximate formulation which involves only the pressure on the boundary of the fluid domain. The two formulations are shown to be in excellent agreement for the case of a long straight duct obstructed by a diaphragm which makes the simplified integral formulation a reliable alternative to usual computational methods. The sound power levels as well as the modal contributions compare favorably with measurements. Moreover, it is shown that the computed radiated sound is independent of the outlet condition of the flow simulation.