For `f(x) = sin x - x^(2) + 1`, check weather the function is increasing, decreasing or has a point of extremum ?

Explanation

To analyze the function \( f(x) = \sin x - x^2 + 1 \) for increasing, decreasing behavior, or points of extremum, we will follow these steps:

### Step 1: Find the derivative of the function
To determine the behavior of the function, we first need to find its derivative \( f'(x) \).

\[ f'(x) = \frac{d}{dx}(\sin x - x^2 + 1) \]
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