IIT JEE Problem

Calculus Level 4

$The\quad value\quad of\quad \int _{ 0 }^{ 1 }{ \frac { { x }^{ 4 }{ (1-x) }^{ 4 } }{ 1+{ x }^{ 2 } } } dx\quad is:$

\frac { 22 }{ 7 } -\pi

-1 0

\frac { 71 }{ 15 } -\frac { 3 }{ 2 } \pi

\frac { 2 }{ 105 } .