By using the properties of definite integrals, evaluate the integrals`int_0^4 |x-1|dx`

Explanation

To evaluate the integral \( I = \int_0^4 |x - 1| \, dx \), we will use the properties of definite integrals and the definition of the absolute value function.

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

### Step 2: Split the integral into two parts.
We can write:
\[
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