Using integration, find the area of the region bounded by the lines `Y = 1 + |x+ 1|, x = -2, x = 3 and y = 0.`

Explanation

To find the area of the region bounded by the lines \( y = 1 + |x + 1| \), \( x = -2 \), \( x = 3 \), and \( y = 0 \), we will follow these steps:

### Step 1: Analyze the Absolute Value Function
The function \( y = 1 + |x + 1| \) can be split into two cases based on the value of \( x \):

1. **Case 1**: When \( x + 1 \geq 0 \) (i.e., \( x \geq -1 \)):
\[
y = 1 + (x + 1) = x + 2
...