2012 Cayley Problem 18

Six consecutive integers are written on a blackboard. When one of them is erased the sum of the remaining five integers is 2012. What is the sum of the digits of the integer that was erased?

\textbf{(A)}\ 5\quad \textbf{(B)}\ 6\quad \textbf{(C)}\ 7\quad \textbf{(D)}\ 9\quad \textbf{(E)}\ 11

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 Cayley contests here.