solution: 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 $\boxed{-2,1}.$
prompt.content: <|im_start|>system
  You are a helpful assistant.<|im_end|>
  <|im_start|>user
  Find all the integer roots of
  \[x^4 + 5x^3 + 9x^2 - x - 14 = 0.\]Enter all the integer roots, separated by commas.
  Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
  <|im_start|>assistant
  
prompt.role: user
extra_info.answer: -2,1
extra_info.question: Find all the integer roots of
  \[x^4 + 5x^3 + 9x^2 - x - 14 = 0.\]Enter all the integer roots, separated by commas.
extra_info.split: test