Answer
$$A = 2$$
Work Step by Step
$$\eqalign{
& f\left( x \right) = \sin x,{\text{ }}\left[ { - \pi /4,3\pi /4} \right] \cr
& {\text{From the graph we can see that the area is given by}} \cr
& A = - \int_{ - \pi /4}^0 {\sin x} dx + \int_0^{3\pi /4} {\sin x} dx \cr
& {\text{Integrate and evaluate}} \cr
& A = - \left[ { - \cos x} \right]_{ - \pi /4}^0 + \left[ { - \cos x} \right]_0^{3\pi /4} \cr
& A = \left[ {\cos x} \right]_{ - \pi /4}^0 - \left[ {\cos x} \right]_0^{3\pi /4} \cr
& A = \cos 0 - \cos \left( { - \frac{\pi }{4}} \right) - \cos \left( {\frac{{3\pi }}{4}} \right) + \cos \left( 0 \right) \cr
& {\text{Simplifying}} \cr
& A = 2 \cr} $$
