Find the area bounded by the curve `y=sin^(-1)x` and the line `x=0,|y|=pi/2dot`

Explanation

To find the area bounded by the curve \( y = \sin^{-1} x \) and the lines \( x = 0 \) and \( |y| = \frac{\pi}{2} \), we can follow these steps:

### Step 1: Understand the curve and the boundaries
The curve \( y = \sin^{-1} x \) is defined for \( x \) in the interval \([-1, 1]\) and takes values from \(-\frac{\pi}{2}\) to \(\frac{\pi}{2}\). The line \( x = 0 \) is the y-axis, and \( |y| = \frac{\pi}{2} \) corresponds to the horizontal lines \( y = \frac{\pi}{2} \) and \( y = -\frac{\pi}{2} \).

### Step 2: Set up the area integral
The area we want to find is above the x-axis and below the curve from \( x = 0 \) to \( x = 1 \). We can express the area \( A \) as:
\[
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