Manipulation of a bounded solid

Calculus 3rd edition, by Smith Minton.

Page 1050, example 2.4:  the solid bounded by z=2, z=(x^2)+1, y=0, and x+y=2.

p1=Graphics[RegionPlot3D[2≥z&&z≥(x^2)+1&&0≤y≤2-x,{x,-1,1},{y,0,3},{z,0,3},PlotPoints->50,Mesh->None]]

p2=Graphics[ContourPlot3D[{z-2==0,(x^2)+1-z==0,y==0,x+y-2==0},{x,-2,2},{y,-2,4},{z,.5,2.5},ContourStyle->Opacity[.8],Mesh->None]]

Show[p2,p1]

Manipulate[Show[{Graphics[ContourPlot3D[{z-2==0,(x^2)+1-z==0,y==0,x+y-2==0},{x,-2,2},{y,-2,4},{z,.5,2.5},ContourStyle->Opacity[a],Mesh->None]],
Graphics[RegionPlot3D[2≥z&&z≥(x^2)+1&&0≤y≤2-x,{x,-1,1},{y,0,4},{z,0,3},PlotPoints->50,Mesh->None]]}],{a,1,0,.5}]