By differentiating \(\mathrm { e } ^ { - x ^ { 2 } }\), find the Maclaurin's series for \(\mathrm { e } ^ { - x ^ { 2 } }\) up to and including the term in \(x ^ { 2 }\).
Deduce an approximation to \(\int _ { 0 } ^ { \frac { 1 } { 5 } } \mathrm { e } ^ { - x ^ { 2 } } \mathrm {~d} x\), giving your answer as a rational fraction in its lowest terms.