Answer
$$\pi - \frac{3}{2}$$
Work Step by Step
$$\eqalign{
& \int_0^{\pi /3} {\left( {3 - 3\sin x} \right)} dx \cr
& {\text{sum rule for integrals}} \cr
& = 3\int_0^{\pi /3} {dx} - 3\int_0^{\pi /3} {\sin x} dx \cr
& {\text{integrate by using the basic integration rule }}\int {\sin x} dx = - \cos x + C\,\,\,\left( {{\text{page 692}}} \right) \cr
& = 3\left( x \right)_0^{\pi /3} - 3\left( { - \cos x} \right)_0^{\pi /3} \cr
& = 3\left( x \right)_0^{\pi /3} + 3\left( {\cos x} \right)_0^{\pi /3} \cr
& {\text{use fundamental theorem of calculus }}\int_a^b {f\left( x \right)} dx = F\left( b \right) - F\left( a \right).\,\,\,\,\left( {{\text{see page 388}}} \right) \cr
& = 3\left( {\frac{\pi }{3} - 0} \right) + 3\left( {\cos \frac{\pi }{3} - \cos 0} \right) \cr
& {\text{simplifying}} \cr
& = 3\left( {\frac{\pi }{3}} \right) + \left( {\frac{1}{2} - 1} \right) \cr
& = \pi - \frac{3}{2} \cr} $$
