I have the following integral: $$\int_{0}^{1/2} e^{x^2}dx$$

i have approximated the 5th degree maclaurin polynomial of the integral to be:

$1+x^2+(1/2)x^4$. I need to obtain an upper bound on the error in the integrand for x in the range $0\le x\le1/2$ when the integrand is approximated by p5(x)

I have deduced p6(x) to be $x^6/6$ but just cant seem to go from here with the formula for obtaining errors.

can someone help me with obtaining the upper limit?

thank you:)