If C is the triangle of vertices (0,0), (1,0) and (1,1) oriented in direction anti-clockwise

$\displaystyle \int_C 2xydx + (x^2+x)dy = ?$

Solution:

$\displaystyle \frac{ \partial (x^2+x)}{ \partial x} - \frac{ \partial (2xy)}{ \partial y} = 1$

$\displaystyle 1 \int \int_D dxdy = \int_0^1 \int_0^1 dxdy = 1$

Correct ????