Answer
$$0$$
Work Step by Step
$$\eqalign{
& \int_{ - \pi }^\pi {\sin x} dx \cr
& {\text{Let }}f\left( x \right) = \sin x \cr
& f\left( { - x} \right) = \sin \left( { - x} \right) \cr
& f\left( { - x} \right) = - \sin x \cr
& f\left( { - x} \right) = - f\left( x \right) \cr
& {\text{The integrand is odd, then using the property }} \cr
& \int_{ - a}^a {f\left( x \right)} dx = 0,\,\,\,f\left( x \right){\text{ is odd,}} \cr
& \cr
& {\text{We obtain}} \cr
& \int_{ - \pi }^\pi {\sin x} dx = 0. \cr
& \cr
& {\text{Graph}} \cr} $$
