Simple line integral Let $f(x,y)=x$ and $C=[0,1]\times\{0\}$ (the line segment joining the point $(0,0)$ and $(1,0)$).
I want to calculate $\boxed{\displaystyle\int_C f(x,y)\,ds}$.

I calculate the following:
$$\displaystyle\int_C f(x,y)\,ds=\int_0^1 x\,dx=\frac{1}{2}$$ its ok?

It is correct if the orientation of the contour is left-to-right (starting at $(0,0)$ and ending at $(0,1)$).
If the orientation is reversed, the value will be $-1/2$.
For line integrals, you should imagine a point in motion along the contour, so there is a "time orientation" of the path. It's not enough to specify the path as a point set, a direction must also be specified (unless the value is zero).
