Nice work, Ronnie.
Here's my full solution as well:

(1) To solve quadratic inequalities, try factoring the expressions.
We get (x+1)(x+3) > 0 Notice that when x=-1 and x=-3, (x+1)(x+3) EQUALS 0.
Now ask, “What happens when x is less than -3?” We see that (x+1)(x+3) will always be positive for these values of x.
Then ask, “What happens when x is between -3 and -1?” We see that (x+1)(x+3) will always be negative for these values of x.
Finally ask, “What happens when x is greater than -1?” We see that (x+1)(x+3) will always be positive for these values of x.
We see that (1) tells us that x can be less than -3 or greater than -1 (not enough information)

(2) Using the same technique as above, we see that -3 > x > -1
Since x is an integer, it must be the case that x= -2 (enough information)

The correct answer is B