The absolute value function $|2x-1|$ is equal to $2x-1$ when $2x-1 \geq 0$ (i.e., $x \geq 1/2$) and is equal to $-(2x-1)$ when $2x-1 < 0$ (i.e., $x < 1/2$). Therefore, we can split the integral as follows:
$$\int_{0}^{2}|2 x-1| d x = \int_{0}^{1/2}-(2x-1) dx +
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