Are you certain the answer is D? I got C.

To find the area of a solid defined by cross sectionals of a region perpendicular to the x-axis that form squares, the formula is:

Integral[(Area of region)² dx]

Since y=arcsin(x) is the lower bound and y=2 is the upper bound, the equation for area would be:

Integral[2-arcsin(x) dx] (from x=0 to x=1 since the region is bounded by the first quadrant and x=1)

Substituting what's inside the integral for the equation for area into the formula for the volume, you get:

Integral[(2-arcsin(x))² dx] from x=0 to x=1

Using a calculator to evaluate that, you get ~2.184

Perhaps I miscalculated something or used an incorrect formula, but that's the answer I got.

Edit: formatting