The key here is that if the vector is constant, there is no need for an integral. Its kind of like when you are integrating a constant function in elementary calculus, you just multiply the value of the function times the change in x.
The same thing applies here. r(b)-r(a) is simply the displacement vector from your start to your end point, and you dot product it with the vector v. Basically since the vector field (v) is constant, you can just have 1 piece in the sum. The dr will be the displacement vector.
You might need to show that the path is irrelevant for constant fields, but that depends on what you are allowed to use.