Consecutive means in order, so 1, 2, 3, 4, 5, etc are all consecutive integers. So you would have to figure out what x+6 is. The numbers would be -1, 0, 1, 2, and 3. They are 5 numbers in a row and when you add them together, you'd get 5, which is exactly 6 more than the smallest number.
Hope this helps!