A thin, non-uniform circular disk of mass \(M\) and radius \(R\) lies in the \(xy\)-plane. The surface mass density \(\sigma(r)\) of the disk varies with radial distance \(r\) from the central axis according to \(\sigma(r) = \sigma_0 \left(1 - \dfrac{r}{R}\right)\), where \(\sigma_0\) is a positive constant. Which of the following expressions correctly gives the rotational inertia \(I\) of the disk about an axis perpendicular to the disk passing through its center?