The invariant mass spectrum of the eta pi^+ pi^- final state produced in two-photon collisions is obtained using a 673 fb^{-1} data sample collected in the vicinity of the Upsilon(4S) resonance with the Belle detector at the KEKB asymmetric-energy e^+e^- collider. We observe a clear signal of the eta_c and measure its mass and width to be M(eta_c)=(2982.7 +- 1.8(stat) +- 2.2(syst) +- 0.3(model)) MeV/c^2 and Gamma(eta_c) = (37.8^{+5.8}_{-5.3}(stat) +- 2.8(syst) +- 1.4(model)) MeV/c^2. The third error is an uncertainty due to possible interference between the eta_c and a non-resonant component. We also report the first evidence for eta(1760) decay to eta pi^+ pi^-; we find two solutions for its parameters, depending on the inclusion or not of the X(1835), whose existence is of marginal significance in our data. From a fit to the mass spectrum using coherent X(1835) and eta(1760) resonant amplitudes, we set a 90% confidence level upper limit on the product Gamma_{gammagamma} BR (eta pi^+ pi^-) for the X(1835).
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