FilledPlot[{h[x],average},{x,a,b}]
FilledPlot[y[x],{x,a,b},Fills->RGBColor[0.5,0.2,0.3]}]
SurfaceOfRevolution[y[x],{x,a,b},RevolutionAxis->{1,0,1}]
Plot[y[x],{x,-1,14},PlotPoints->1000,AspectRatio->0.5,
Background->RGBColor[1,1,0.9], GridLines->Automatic]