Area ( parametric curves )

Question

Sketch the parametric curve x = t², y = t(t−1)(t + 1) and find the area enclosed by its loop.

 

I dont understand why the limits of integration are 0 to -1 ?

 

Answer 1

x = t^2

y= t(t-1)(t+1) = t(t^2-1)

x=y when t^2 = t^3 -t which happens at t= 0 and t=-1