Since open sets do not contain their boundary, their compliment must contain all points that are in the boundary of the original set (where open) and not contain the boundary when it's there (when closed).
Think of the interval as a set of points. Note that -2 is in A and 1 is not in A. This means must contain -2, but can't contain 1.
Your answer is not correct. The answer is . -2 can't be in because it's in . 1 must be in because it isn't in . Is that clear? The compliment is just the set of points that aren't in its base.