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 $10 ^ { - 3 }$ .
- $$F ( x ) = \int _ { 0 } ^ { x } e ^ { - t ^ { 2 } } d t , [ 0,0.5 ]$$

A) $x + \frac { x ^ { 3 } } { 3 } + \frac { x ^ { 5 } } { 5 }$
B) $x - \frac { x ^ { 3 } } { 3 } + \frac { x ^ { 5 } } { 10 }$
C) $x - \frac { x ^ { 3 } } { 3 } + \frac { x ^ { 5 } } { 15 }$
D) $x - \frac { x ^ { 3 } } { 3 } + \frac { x ^ { 5 } } { 5 }$