The area (in sq. units) in the first quadrant bounded by the curve $y=x^2+2$ and the lines $y=x+1$,$x=0$,and $x=2$ is:
- A$\frac{1}{3}$
- B$\frac{2}{3}$
- C$\frac{5}{3}$
- D$\frac{8}{3}$
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