Evaluate the following integral: `int_0^4|x-1|dx`

Explanation

To evaluate the integral \( \int_0^4 |x-1| \, dx \), we need to analyze the expression inside the absolute value, \( |x-1| \).

### Step 1: Determine where the expression changes
The expression \( |x-1| \) changes at \( x = 1 \). We need to split the integral into two parts based on this point:
- From \( 0 \) to \( 1 \), \( x-1 \) is negative, so \( |x-1| = -(x-1) = 1-x \).
- From \( 1 \) to \( 4 \), \( x-1 \) is positive, so \( |x-1| = x-1 \).

### Step 2: Set up the integral
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