We report on a detailed investigation of the high-energy gamma-ray emission from NGC,1275, a well-known radio galaxy hosted by a giant elliptical located at the center of the nearby Perseus cluster. With the increased photon statistics, the center of the gamma-ray emitting region is now measured to be separated by only 0.46 from the nucleus of NGC1275, well within the 95% confidence error circle with radius ~1.5. Early Fermi-LAT observations revealed a significant decade-timescale brightening of NGC1275 at GeV photon energies, with a flux about seven times higher than the one implied by the upper limit from previous EGRET observations. With the accumulation of one-year of Fermi-LAT all-sky-survey exposure, we now detect flux and spectral variations of this source on month timescales, as reported in this paper. The average >100 MeV gamma-ray spectrum of NGC1275 shows a possible deviation from a simple power-law shape, indicating a spectral cut-off around an observed photon energy of E = 42.2+-19.6 GeV, with an average flux of F = (2.31+-0.13) X 10^{-7} ph/cm^2/s and a power-law photon index, Gamma = 2.13+-0.02. The largest gamma-ray flaring event was observed in April--May 2009 and was accompanied by significant spectral variability above E > 1-2 GeV. The gamma-ray activity of NGC1275 during this flare can be described by a hysteresis behavior in the flux versus photon index plane. The highest energy photon associated with the gamma-ray source was detected at the very end of the observation, with the observed energy of E = 67.4GeV and an angular separation of about 2.4 from the nucleus. In this paper we present the details of the Fermi-LAT data analysis, and briefly discuss the implications of the observed gamma-ray spectral evolution of NGC1275 in the context of gamma-ray blazar sources in general.
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