Use a power series to approximate the definite integral to six decimal places

Use a power series to approximate the definite integral to six decimal places?

Integral from 0 --> .3 of (( x^2 ) / (1 + x^4)) dx

Not sure how to do this problem, please help. Please show your steps so i can follow what you do. Thanks so much for all the help!!

1/(1+x^4) = 1 - x^4 + x^8 - x^12 + x^16...
x^2/(1+x^4) = x^2 - x^6 + x^10 - x^14 + x^18...
Integrate:x^3/3 - x^7/7 + x^11/11 - x^15/15 + x^19/19...
Plug in 0.3 in for x: 0.009 - 0.000031243 + 0.000000161 - 0.000000001 = 0.008968917