Questions on Taylor series and CAS integrate

[factor]

While trying to repeat a Taylor series calculation for approximation (link) on the Prime, the following results are obtained:

   

i.e.
taylor(e^(-x²/2),x,6)

returned result:
1-(1/2)*x²+(1/8)*x^4-(1/48)*x^6+(1/384)*x^8-(1/3840)*x^10+(1/46080)*x^12+x^14*order_size(x)

and then integrate the result (the last term "order_size(x)" removed):
int(1-(1/2)*x²+(1/8)*x^4-(1/48)*x^6+(1/384)*x^8-(1/3840)*x^10+(1/46080)*x^12)


The answer is:
(231*x^13-3276*x^11+40040*x^9-411840*x^7+3459456*x^5-23063040*x^3+138378240*x)/138378240


Got two questions from the results and would be grateful for any advice..

1) what is the last term order_size(x) from the returned Taylor polynomial? Are there anyway to prevent it from returning?

2) in the last integration, the resulting equation is quite dissimilar to the one as in the link above (which is from the other brand calculator). Prime returned one with 7 multiplications with very large numbers, plus one division, while the other result looks more compact with only 6 divisions with relatively smaller numbers. Looks like Prime's CAS choose to have one common denominator and hence a very large one. Are there way to somehow simplify the Prime's result?

Thanks in advance!