Evaluate the following integral: `int_0^1|2x-1|d` x

Explanation

To evaluate the integral \( \int_0^1 |2x - 1| \, dx \), we need to analyze the expression inside the absolute value, \( |2x - 1| \).

### Step 1: Determine where the expression changes sign
The expression \( 2x - 1 \) changes sign at the point where it equals zero:
\[ 2x - 1 = 0 \implies 2x = 1 \implies x = \frac{1}{2} \]

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