Proof Writing & Problem Solving · Challenge problem

For how many integers $c$ with $-10 \le c \le 10$ is exactly one of the following two statements true?

(I) For every real $x$ there is a real $y$ with $y^2 + xy = c$.

(II) There is a real $y$ such that for every real $x$, $y^2 + xy = c$.