Evaluate the following integral: `int_(-6)^6|x+2|dx`

Explanation

To evaluate the integral \( I = \int_{-6}^{6} |x + 2| \, dx \), we will first analyze the expression inside the absolute value to determine the points where it changes sign.

### Step 1: Identify the critical point
The expression \( |x + 2| \) changes sign at \( x + 2 = 0 \), which gives us \( x = -2 \). This point divides the integral into two parts: from \(-6\) to \(-2\) and from \(-2\) to \(6\).

### Step 2: Break the integral into two parts
We can express the integral as:
\[
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