I'm looking at an example in my notes where the line integral of two segments is being evaluated so (integral)C=(integral)C1+(integral)C2.

For c1 : segment between (0,0) and (1,1)

For c2: part of the parabola y = sqrt(x) between (1,1) and (4,2)

for the parameterization it's written:

c1: x(t) = t, y(t) = t, 0<=t<=1

c2: x(t) = tē, y(t) = t, 1<=t<=2

Can someone explain to me how to get that parameterization?