#### Answer

$\approx 0.824$

#### Work Step by Step

The area of under $y=f(x)$ over an interval $[m,n]$ about the x-axis is given by:
$Area, A= \int_{0.83}^{\pi} (\sin x -(1-\dfrac{x}{\pi})) \ dx \\ = \int_{0.83}^{\pi} [\sin x -1+\dfrac{x}{\pi})] \ dx \\=[-\cos x -x+\dfrac{x^2}{2 \pi}]_{0.83}^{\pi}$
Now, we will use a graphing calculator to obtain the approximate value of the area.
So, $Area, A \approx 0.824$