Answer
$f(-2)=4$
$f(-1)=1$
$f(0)=1$
$f(1)=2$
$f(2)=3$
Work Step by Step
Because x=-2, x=-1 are in between $(-\infty,0)$ of $f(x)=x^{2}$
so $f(-2)=(-2)^{2}=4$
$f(-1)=(-1)^{2}=1$
x=0, x=1 and x=2 are in between $[0,+\infty)$ of $f(x)=x+1$
So $f(0)=0+1=1$
$f(1)=1+1=2$
$f(2)=2+1=3$