Line Integral of a Vector Field in 3-Space

This worksheet illustrates the integral of a vector field along a closed curve in 3-space. You may rotate the view by clicking and dragging.
What does the (animated) blue arrow represent?
What does the (animated) red arrow represent?
Suppose that [math]\vec{F}\left(x,y,z\right)[/math] and [math]C[/math] denote, respectively, the vector field and curve displayed above. Then value of [math]\int_C\vec{F}\left(x,y,z\right)\cdot ds[/math] is the "sum" of which quantities?
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– Kristen Beck

Information: Line Integral of a Vector Field in 3-Space