using two dy integral rotate according to y axis

Question

Let R be the region in the first quadrant bounded by the curves

y = f(x) = 2x+ 1 

y = g(x) = 2x^2 − 8x + 9

Find the volume of the solid obtained by rotating the region R about y-axis using two dy-integral.

1) I am in trouble to use two dy integral according to y axis. I guess 1 to 3 and 3 to 9 it should be

Answer 1

desmos.com/calculator/5axg1l05ta

Video shows 2nd integral as from 3 to 9, but should have been from 1 to 3.