X-ray flux distributions of M31 sources detected in the southern (top row) and northern (bottom row) deep fields in the northern disc. Left panels: X-ray flux functions, along with power law and cut-off power law fits. Right panels: combined flux distribution expected from sources in flux bins, normalised for the deep field areas. The unresolved flux per unit area is determined by integrating over this distribution and subtracting the flux of detected sources.