Hint) Verify that I is an ideal, written <x^2 +1>. Since x^2 + 1 is irreducible inR=R[x] andRis PID, <x^2 +1> is a maximal ideal inRIt follows thatR[x]/<x^2+1> is a field. Let . Then, an elements ofR[x]/<x^2+1> has the form , where k_1, k_2R. I leave it to you to fill the remaining steps.