Answer
$| Error| \lt 0.00064$
Work Step by Step
Integrate the integral with respect to $ x $ as follows:
$ f(x)=\int_0^{x} t^2 e^{-t^2} \space dt \space \\=\int_0^{x} [t^2-t^4+\dfrac{t^6}{2 !} -\dfrac{t^{8}}{3!}-...] \space dt \\ =\dfrac{x^3}{3}-\dfrac{x^{5}}{5}+\dfrac{x^{7}}{7 \cdot 2!}-\dfrac{x^{9}}{9 \cdot 3!}+\dfrac{x^{11}}{11 \cdot 4!} ....$
Now, the error can be found as follows:
$| Error| \lt \dfrac{1}{13\cdot 5 !} \approx 0.00064$
and $| Error| \lt 0.00064$
