Differential cross sections have been extracted from exclusive and kinematically complete high-statistics measurements of quasifree polarized (n) over barp scattering performed in the energy region of the d* (2380) dibaryon resonance covering the range of beam energies T-n = 0.98-1.29 GeV (root s = 2.32-2.44 GeV). The experiment was carried out with the WASA-at-COSY setup having a polarized deuteron beam impinged on the hydrogen pellet target and utilizing the quasifree process dp -> np + p(spectator). In this way the np differential cross section sigma (Theta) was measured over a large angular range. The obtained angular distributions complement the corresponding analyzing power A(y)(Theta) measurements published previously. A SAID partial-wave analysis incorporating the new data strengthens the finding of a resonance pole in the coupled D-3(3) - (3)G(3) waves.