JEE Math Practice Question

Let f be a differentiable function from R to R such that $$\left| {f\left( x \right) - f\left( y \right)} \right| \le 2{\left| {x - y} \right|^{{3 \over 2}}},$$ for all $$x,y \in $$ R. If $$f\left( 0 \right) = 1$$ then $$\int\limits_0^1 {{f^2}} \left( x \right)dx$$ is equal to :

1. A.1
2. B.2
3. C.$${1 \over 2}$$
4. D.0