Answer:
D
Step-by-step explanation:
Set up to different integrals that match the endpoints
so in our case it would look like
[tex]\int\limits^0_{-2} {x} \, dx +\int\limits^1_0 {x+1} \, dx[/tex]
now it's just a matter of computing it
[tex]\int\limits^0_{-2} {x} \, dx =x^2\\0^2-(-2)^2=4\\\int\limits^1_0 {x+1} \, dx =\frac{x^2}{2}+x\\\frac{1}{2}+1-0=\frac{3}{2}\\\frac{3}{2}+4=\frac{11}{2}[/tex]
