We report a fully inclusive measurement of the flavour changing neutral current decay b->s gamma in the energy range 1.8 GeV < E* < 2.8 GeV, covering 95% of the total spectrum. Using 140 fb^-1 we obtain BF(b->s gamma)= 3.55 +/- 0.32 +0.30-0.31 +0.11-0.07, where the errors are statistical, systematic and from theory corrections. We also measure the first and second moments of the photon energy spectrum above 1.8 GeV and obtain <E> = 2.292 +/- 0.026 +/- 0.034 GeV and <E^2>-<E>^2 = 0.0305 +/- 0.0074 +/- 0.0063 GeV^2, where the errors are statistical and systematic.