If the line $$x=\alpha$$ divides the area of region $$R={(x,y)\epsilon R^{2}:x^{3}\leq y\leq x},0\leq x\leq1$$ into two equal parts, then

A

$$0<\alpha \leq\frac{1}{2}$$

B

$$\frac{1}{2}<\alpha<1$$

C

$$2\alpha^{4}-4\alpha^{2}+1=0$$

D

$$\alpha^{4}+4\alpha^{2}-1=0$$