I am fairly new to this so...

$\displaystyle \int_{-3}^0(1+\sqrt{9- x^{2}})dx

\Rightarrow

\int_{-3}^{0}1dx + \int_{-3}^0\sqrt{9- x^{2}}dx

\Rightarrow

3 + \int_{-3}^0\sqrt{9- x^{2}}dx

$

assuming the form (from the reference in back of book)

$\displaystyle

\int_{}{}\sqrt{a^2- u^2}du

= \frac{u}{2}\sqrt{a^2-u^2}+\frac{a^2}{2}\sin^{-1}{\frac{u}{a}+C

$

would be the way to solve the rest of it

but don't seem to get the answer of $\displaystyle 3+\frac{9\pi}{4}$