We report a fully inclusive measurement of the flavor changing neutral current decay b --> sgamma in the energy range 1.8 GeV < or = E*gamma < or = 2.8 GeV, covering 95% of the total spectrum. Using 140 fb(-1), we obtain B(b --> sgamma) = (3.55+/-0.32(+0.30+0.11)(-0.31-0.07)) x 10(-4), 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 (Egamma) = 2.292+/-0.026+/-0.034 GeV and (E2gamma) - (Egamma)2 = 0.0305+/-0.0074+/-0.0063 GeV2, where the errors are statistical and systematic.