Integrate[4-x-y,{y,0,1}]

Integrate[
Integrate[4-x-y,{y,0,1}]
,{x,0,2}
]

Integrate[Sqrt[1-x^2]-(1-x),x]

myArea=Integrate[Sqrt[1-x^2]-(1-x),{x,0,1}]

p1=ParametricPlot3D[{x,1-x,z},{x,0,1},{z,0,1},PlotStyle->{Red,Opacity[0.5]}]

p2=ParametricPlot3D[{x,Sqrt[1-x^2],z},{x,0,1},{z,0,1},PlotStyle->{Orange,Opacity[0.5]}]

p3=ParametricPlot3D[{x,y,1},{x,0,1},{y,0,1},PlotStyle->{Blue,Opacity[0.5]}]

p4=ParametricPlot3D[{x,y,x},{x,0,1},{y,0,1},PlotStyle->{Blue,Opacity[0.5]}]

Show[p1,p2,p3,AxesLabel->{x,y,z}]

Show[p1,p2,p4,AxesLabel->{x,y,z}]

f[x_]:=-(x-8)*(3x-9)*(x-5)*(x-7)+30
Integrate[f[x],{x,3,8.}]/5
Plot [{f[x],36.25},{x,2,10},PlotRange->{-10,80},GridLines->{{3,8},{}}]