If $x^2+ax+b$ is an integer for every integer $x$ then comment on the coefficients $a$ and $b$ MCQ

If $x^2+ax+b$ is an integer for every integer $x$ then comment on the
coefficients $a$ and $b$ MCQ

Probably a more general category (number theory) multiple choice question
but no clue how to get to a clear conclusion . Here's how it goes :
Q) If $x^2+ax+b$ is an integer for every integer x then :
(A)$a$ is always an integer but $b$ need not be an integer
(B)$b$ is always an integer but $a$ need not be an integer
(C)$a$ and $b$ are non-integers but a+b should always be an integer
(D)Both $a$ and $b$ are integers
Please guide me on how to solve this/similar questions.
Thanks.