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Question is related to line integration, work done by force from book Erwin krezyick advance maths

I cannot understand how to write my function in the form of r(t)
Can u please solve these questions and teach me?
Q:calculate intgeral of F(r(t)). r'(t)
Qno1. F=[xy,x²y²] , C the straight line segment from (0,2) to (2,0)
Qno2.F=[(x-y)², (y-x)²], C; xy=1  1≤x≤4
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1 Answer

For Question 1
Use the following parameterization:
r(t) = <x0,y0>(1-t) + <x1,y1>t
Where (x0,y0) be the starting point of the line segment.
And (x1,y1) be the end point of the line segment.
(Keep in mind <x0,y0> is a vector = x0 i + y0 j)
In this case, (x0,y0) = (0,2) and (x1,y1) = (2,0)
= <0,2>(1-t) + (2,0)t
= <0, 2(1-t)> + <2t, 0>
= <2t, 2-2t>
dr/dt = <2, -2> dt