The sum of seven integers is $-1$. What is the maximum number of the seven integers that can be larger than $13$?
$\textbf{(A)}\ 1\qquad\textbf{(B)}\ 4\qquad\textbf{(C)}\ 5\qquad\textbf{(D)}\ 6\qquad\textbf{(E)}\ 7$
If the first six integers are $14$, the last number can be $(-14\cdot 6) - 1 = -85$.  The sum of all seven integers will be $-1$.
However, if all seven integers are over $13$, the smallest possible sum is $14\cdot 7 = 98$.
Thus, the answer is $6$, which is option $\boxed{D}$.