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