By the Integer Root Theorem, the possible integer roots are all the divisors of 14 (including negative divisors), which are $-14,$ $-7,$ $-2,$ $-1,$ $1,$ $2,$ $7,$ and $14.$  Checking, we find that the only integer roots are $-2,1.$
Find all the integer roots of
\[x^4 + 5x^3 + 9x^2 - x - 14 = 0.\]Enter all the integer roots, separated by commas.