Find the Polynomial of Lowest Degree That Will Approximate $F ( x )$

Find the polynomial of lowest degree that will approximate $F ( x )$ throughout the given interval with an error of magnitude less than than $10 ^ { - 3 }$ .
- $$F ( x ) = \int _ { 0 } ^ { x } \left( \tan ^ { - 1 } t \right) ^ { 2 } d t , [ 0,0.5 ]$$

A) $\frac { x ^ { 3 } } { 3 } - \frac { 2 x ^ { 9 } } { 27 }$
B) $\frac { x ^ { 3 } } { 3 } - \frac { 2 x ^ { 15 } } { 15 }$
C) $\frac { x ^ { 3 } } { 3 } - \frac { 2 x ^ { 9 } } { 9 }$
D) $\frac { x ^ { 3 } } { 3 } - \frac { x ^ { 15 } } { 15 }$