`int_(-pi//2)^(pi//2)"sin"|x|dx` is equal to `1` (b) `2` (c) `-1` (d) `-2`

Explanation

To evaluate the integral \( I = \int_{-\frac{\pi}{2}}^{\frac{\pi}{2}} \sin |x| \, dx \), we can break it down into two parts based on the definition of the absolute value function.

### Step 1: Split the Integral
Since \( |x| \) is defined as:
- \( |x| = -x \) for \( x < 0 \)
- \( |x| = x \) for \( x \geq 0 \)

We can split the integral into two parts:
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