(x+3)² will always be positive.
The only integers less than or equal to 1 are 0 and 1.
How can (x+3)² = 0 ? ---> x = -3
How can (x+3)² = 1 ? ---> (x + 3) = 1 or (x + 3) = -1 ---> x = -4 or x = -2
Answer: 3 integers: -2, -3, and -4