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Let $f$ be a differentiable function from $\mathbb{R}$ to $\mathbb{R}$ such that $|f(x) - f(y)| \leq 2|x - y|^{3/2}$, for all $x, y \in \mathbb{R}$. If $f(0) = 1$ then $\int_0^1 f^2(x),dx$ is equal to:
(1) $1$
(2) $2$
(3) $\dfrac{1}{2}$
(4) $0$
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