I don't understand what this line in my textbook is saying. Here's the quote:
If the integrand $\vec A.d\vec r$ is a perfect differential dN, then
$$\int_C \vec A.d\vec r=\int^{(c,d)}_{(a,b)}dN=N(c,d)-N(a-b)$$
Can someone help me interpret this? $\vec A$ is the vector field, $\vec r$ is the vector equation of the line.
By the way, this appears in the 'evaluation of line integrals for plane curves' section of my textbook.