Answer
\[2 - \pi \]
Work Step by Step
\[\begin{gathered}
\int_{ - \pi /2}^{\pi /2} {\left( {\cos x - 1} \right)} dx \hfill \\
\hfill \\
{\text{integrating}} \hfill \\
\hfill \\
\left[ {\sin x - x} \right]_{ - \pi /2}^{\pi /2} \hfill \\
\hfill \\
{\text{Use the fundamental theorem of calculus}} \hfill \\
\hfill \\
\left[ {\sin \left( {\frac{\pi }{2}} \right) - \frac{\pi }{2}} \right] - \left[ {\sin \left( { - \frac{\pi }{2}} \right) + \frac{\pi }{2}} \right] \hfill \\
\hfill \\
{\text{Simplify}} \hfill \\
\hfill \\
1 - \frac{\pi }{2} + 1 - \frac{\pi }{2} \hfill \\
\hfill \\
2 - \pi \hfill \\
\end{gathered} \]
