`int_(0)^(1) sin^(-1) x dx =(pi)/(2) -1`

Explanation

To solve the integral \( \int_{0}^{1} \sin^{-1} x \, dx \) and show that it equals \( \frac{\pi}{2} - 1 \), we will use a substitution and integration by parts.

### Step-by-Step Solution:

1. **Substitution**: Let \( x = \sin \theta \). Then, \( dx = \cos \theta \, d\theta \).
- When \( x = 0 \), \( \theta = 0 \).
- When \( x = 1 \), \( \theta = \frac{\pi}{2} \).

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