Evaluate the integral by interpreting it in terms of areas.

37. $\displaystyle \int^0_{-3} (1+\sqrt{9-x^2})*dx$

the answer is $\displaystyle 3+\frac{9}{4}*\pi$

Where .. the heck did $\displaystyle \pi$ come from?

I was trying to do

$\displaystyle \frac{b-a}{n}$

$\displaystyle = \frac{0-3}{n}$

$\displaystyle =\frac{-3}{n}$

and then $\displaystyle x_{i}$ as $\displaystyle \frac{-3i}{n}-3$

then plugging $\displaystyle x_{i}$ into $\displaystyle f(x)*dx$ then solving for the limit. It came out to be a super complicated root problem so I look in the back to see if I'm in the right track.. and theres a $\displaystyle \pi$ in the answer...

I think I'm missing something here... how is this integral end up having a $\displaystyle \pi$?