2014 Fermat Problem 10

A line segment of length 5 lies along the number line initially between 1 and 6.

The line segment is rotated 180^\circ about the point at 2. The resulting line segment lies between -2 and 3. This segment is then rotated 180^\circ about the point at 1. The resulting line segment lies between

\textbf{(A)}\ -2 \text{ and } 3\quad \textbf{(B)}\ -1 \text{ and } 4\quad \textbf{(C)}\ 0 \text{ and } 5\quad \textbf{(D)}\ -3 \text{ and } 2\quad \textbf{(E)}\ -4 \text{ and } 1

If there are no answer choices shown, enter a numerical answer.

Full credit to this problem is given to the CEMC, you may view all Fermat contests here.