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Say $f$ is uniform in $[0,1/2]$, $g$ is uniform in $[0,1]$, and $h$ is uniform in $[1/2,1]$. Then you get

$$ \int_0^{1/2} \frac{2\cdot 1}{2+1} - \int_{1/2}^{1} \frac{1\cdot 2}{1+2} dx +\int_{\emptyset} dx = \frac 1 3 + \frac 1 3 - 0 = \frac 2 3 $$