Answer
2+$\frac{\pi}{2}$
Work Step by Step
y=1+$\sqrt{1-x^2}$
y-1=$\sqrt{1-x^2}$
(y-1)$^2$=1-x$^2$
$x^2$+(y-1)$^2$=1 is the upper Semicircle.
the area of this semicircle is
A=$\frac{1}{2}\pi r^2$
=$\frac{1}{2}\pi(1)^2$=$\frac{\pi}{2}$
The area of the rectangle base is
A=$Lw$ =(2)(1)=2.
Then the total area is 2+$\frac{\pi}{2}$ =>$\int_{-1}^1(1+\sqrt{1-x^2})dx$
=$2+\frac{\pi}{2}$ square units
as shown in given diagram
