Well, this is not the whole question, you need to post the whole thing; help us so we can help you.
I would evaluate each part of the piecewise funtion separately. The only confusing part would be if you were asked to evaluate the function as the limit approaches 1.
The first one (1-x) approaches 0, whereas the second (x+2) approaches 3. So we say there is a discontinuity at x=1. There is not a discontinuity at x=3, because in both your second (x+2) and third (x^2 -4) part, the limit approaches 5