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Integrating a vector? Array? Something else? What even is this?

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Is this a physics class? It looks like the kind of abuse of notation common in physics.

I would say that this is an integral of something along a path that goes from (4, 0) to (6, 1). Often in physics when you have a path integral like that, it doesn't matter what exact path you take. The variable of integration is ds, a parameter that runs along the path, whatever it is.

And typically you'll then choose a path that makes the integration easier. It looks like that happened here. They have an integral in two parts, one that is with respect to x and one with respect to y. So this seems to be specifying a particular path from (4, 0) to (6, 1), one that is first along the x direction from (4, 0) to (6, 0), and then from there in the y direction from (6, 0) to (6, 1).

Alternately you could go up from (4, 0) to (4, 1) and over from (4, 1) to (6, 1). If the integral is indeed independent of the path it shouldn't matter.
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It’s probably a line integral from (4,0) to (6,1).

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