I'm trying to find the moment of inertia of just the quarter circle part for the x1, x2 axis, which I believe would be (being $\rho$ the density): $$\frac{\rho}{16}\pi+\frac{\pi\rho}{4}(1-\frac{4}{3\pi})^2$$
However I am told that it is instead $$\frac{\rho}{16}\pi+\frac{\pi\rho}{4}(-(\frac{4}{3\pi})^2+(1-\frac{4}{3\pi})^2)$$
My question is where does the extra $-(\frac{4}{3\pi})^2$ come from? Does it have to do with the quarter circle being rotated in comparison to the ones shown in tabled values? What am I doing wrong?