Find all integer solutions of $y^2=1+x+x^2+x^3+x^4$

Question

Find all integer solutions of $y^2=1+x+x^2+x^3+x^4$. I tried moving $x^4$ to the other side and factoring the LHS to get $(y+x^2)(y-x^2)=(x+1)(x^2+1)$, but I don't know what to do with that, or if it's even the right thing to do. Please help me out!