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 :