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 $10 ^ { - 3 }$ .
- $$F ( x ) = \int _ { 0 } ^ { x } \frac { \ln \left( 1 + t ^ { 2 } \right) } { t } d t , [ 0,0.6 ]$$

A) $\frac { x ^ { 2 } } { 2 } - \frac { x ^ { 4 } } { 4 } + \frac { x ^ { 6 } } { 6 }$
B) $\frac { x ^ { 2 } } { 2 } - \frac { x ^ { 4 } } { 16 } + \frac { x ^ { 6 } } { 128 }$
C) $\frac { x ^ { 2 } } { 2 } - \frac { x ^ { 4 } } { 8 } + \frac { x ^ { 6 } } { 32 }$
D) $\frac { x ^ { 2 } } { 2 } - \frac { x ^ { 4 } } { 8 } + \frac { x ^ { 6 } } { 18 }$