evaluate :D

$I=\int_C[(x+y^2)\ \mathrm dx+(y-x^2)\ \mathrm dy]$

$x=t\implies\mathrm dx=\mathrm dt$

$y=t^2+1\implies\mathrm dy=2t\ \mathrm dt$

$\displaystyle I=\int_0^1[(t+(t^2+1)^2)\ \mathrm dt+(t^2-t^2+1)2t\mathrm dt]$

$\displaystyle I=\int_0^1(t^4+2t^2+3t+1)\ \mathrm dt$

$\displaystyle I=\frac{101}{3}$