Let f be a differentiable function from R to R such that $\left|f\left(x\right)-f\left(y\right)\right|\le 2{\left|x-y\right|}^{\frac{3}{2}}$for all x, y $\epsilon$ R. If f(0) = 1

then $\underset{0}{\overset{1}{\int }}{f}^2\left(x\right)dx$ equal to