Evaluate the following integral: `int_(-3)^3|x+1|dx`

Explanation

To evaluate the integral \( \int_{-3}^{3} |x + 1| \, dx \), we need to analyze the absolute value function and break the integral into parts where the expression inside the absolute value changes sign.

### Step 1: Identify the points where the expression changes sign
The expression \( |x + 1| \) changes sign at \( x = -1 \). Therefore, we will split the integral at this point.

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