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$\int_{0}^{2}\,f(x)dx = 1$

$\therefore F(2)-F(0) = 1$

$\int_{0}^{1}\,f(2x)dx$

ให้ $u = 2x \Rightarrow \frac{du}{dx} = 2 \Rightarrow dx = \frac{du}{2}$

$\int_{0}^{1}\,f(2x)dx = \int_{0}^{2}\,f(u)\frac{du}{2} = \frac{1}{2} [F(2)-F(0)] = \frac{1}{2} $