With these it is crucial to draw the picture.

You have is a parabola at the top. See the attached image.

So method by washers: the washers are perpendicular to the axis of rotation. So they are horizontal in this case, and integration is parallel to the axis of rotation (so we need x's as a function of y).

With washers you need to figure you the two radii (inner and outer).

Since the axis of rotation is the line x=0, we need the distances from this line.

From y=0 to y=1, inner radius is 0, outer is 1 (note that the

From y=1 to y=2, inner radius is ?, outer is 1

Let's figure out the inner radius: we need to write the inner radius is a function of y. What we have is

but this is the positive one (the curve is for positive x) so

From y=1 to y=2, inner radius is , outer is 1

Now (informally) the volume of the washer is whereRis the outer andris the inner radii.

So

Make sense?