Evaluate: `intcos^(-1)(sinx)\ dx`

Explanation

To evaluate the integral \( I = \int \cos^{-1}(\sin x) \, dx \), we can follow these steps:

### Step 1: Simplify the Integral
We start with the integral:
\[ I = \int \cos^{-1}(\sin x) \, dx \]
Using the identity \( \cos^{-1}(\sin x) = \frac{\pi}{2} - x \) (since \( \sin x = \cos\left(\frac{\pi}{2} - x\right) \)), we can rewrite the integral as:
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