Let R be the region bounded by  $y{x}^4-1+y\le 0,y\ge 0and 0\le x\le 1$. If  $S_R$  be the area of region R, then which of the following statement(s)  is (are) TRUE?

$y\le \frac{1}{x^4+1}, x\le 1, y\ge 0$ so region R is shaded in
Given figure  $\frac{dy}{dx}=\frac{-4x^3}{(x^4+1)}\downarrow$

$\frac{d^{2}y}{d{x}^2}=0 at x={\left(\frac{3}{5}\right)}^{\frac{1}{4}}$ (inflection)
A)  $S_R\ge$ sum of area of rectangles OYPZ and TGXZ
 $\ge \frac{5}{8}\sqrt{\sqrt{\frac{3}{5}}}+\frac{1}{2}(1-\sqrt{\sqrt{\frac{3}{5}}})\ge \frac{1}{8}\sqrt{\sqrt{\frac{3}{5}}}+\frac{1}{2}$
B)  $S_R\le$  sum of area of rectangles OQNZ and PMXZ
  $\le \sqrt{\sqrt{\frac{3}{5}}}+\frac{5}{8}(1-\sqrt{\sqrt{\frac{3}{5}}})\le \frac{5}{8}+\frac{3}{8}\sqrt{\sqrt{\frac{3}{5}}}$
C)  $S_R\ge$ area of trapezium OQPZ   $\ge \frac{1}{2}(1+\frac{5}{8})\sqrt{\frac{3}{5}}\ge \frac{13}{16}\sqrt{\sqrt{\frac{3}{5}}}$
D)   $\because S_R=\underset{0}{\overset{1}{\int }}\frac{dx}{x^4+1}\ge \underset{0}{\overset{1}{\int }}\frac{dx}{x^2+1}\ge \frac{\pi }{4}$