Tensor of inertia of a curved beam

Question

I need help calculating the inertia tensor for a curved beam.

I found the formulas for this in the article https://hal.archives-ouvertes.fr/hal-01084693/document[page 20, Appendix A] and decided to check their correctness. And found the following:

1. The formula for calculating the distance $\chi$ from point $O$ to the center of mass works correctly (tested in SolidWorks using mass analysis);

2. The integration result does not correspond to the original integration formula for the inertia tensor components $I_{yy}$ and $I_{zz}$. $I_{xx}$ component works well when I align the $r$ vector (shown in the picture) with the $x$-axis. This corresponds to my tasks and there are no questions here yet.

3. As far as I understood from the text, this tensor was searched for by placing the origin of coordinates in the center of mass.

My question is: How to find the inertia tensor during the rotation of a curved arc around the point O and, if possible, recalculate it for any point?