Consider the polynomial
$$f ( x ) = 1 + 2 x + 3 x ^ { 2 } + 4 x ^ { 3 }$$
Let s be the sum of all distinct real roots of $\mathrm { f } ( \mathrm { x } )$ and let $\mathrm { t } = | \mathrm { s } |$.
The area bounded by the curve $y = f ( x )$ and the lines $x = 0 , y = 0$ and $x = t$, lies in the interval\\
A) $\left( \frac { 3 } { 4 } , 3 \right)$\\
B) $\left( \frac { 21 } { 64 } , \frac { 11 } { 16 } \right)$\\
C) $( 9,10 )$\\
D) $\left( 0 , \frac { 21 } { 64 } \right)$