∫c (x^2+y^2)dx + (x^2+y^2)dy , C is defined by y=x , y=(1/6)x^2 , 0<x<6

For the limits I'm doing dydx, so:

y is from 0 to x

x is from 0 to 6

∫c (x^2+y^2)dx + (x^2+y^2)dy

= ∫∫2x-2y dydx = 2xy-y^2 from 0 to x

= ∫x^2 dx = (1/3)x^3 from 0 to 6 = 72.

I got it wrong... what did I do wrong and what is the correct answer?