Grassmann's variables under integration

I am not sure that $d(\eta^2)$ is defined at all. But if it is, then, in my opinion, you should write it in this way $$ d(\eta^2) = d(\eta\eta) = d\eta\ \eta + \eta\ d\eta $$ So you get not $\eta\ d\eta = 0$, but natural anticommutation of $\eta$ and $d\eta$: $d\eta\ \eta + \eta\ d\eta = 0$. I think the latter equality is usual for Grassmann integrals.