Since the two integers are consecutive, we can let the first be x and the second be x+1. Then [x] + [x+1] = -225. Simplifying, 2x + 1 = -225, or
2x = -226. Thus, x = -113 and x+1 = -113+1 + -112.
The two consecutive integers are -112 and -113. Adding these together results in -225, as we had hoped.