Here's a region R plotted in the xy-plane. Clear [y]; Rplot = ParametricPlot[{{y (y - 6) + 1, y}, {Cos[ (Pi y)/6]^2, y}}, {y, 0, 6}, PlotStyle ->...
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I have no idea how to set the bounds of integration. The 2 functions that make up this shape are y(y-6)+1 and

[cos(pi*y)/6]^2Screen Shot 2019-10-01 at 5.57.01 PM.png

Screen Shot 2019-10-01 at 5.57.01 PM.png

Here's a region R plotted in the xy-plane.
Clear [y];
Rplot = ParametricPlot[{{y (y - 6) + 1, y}, {Cos[ (Pi y)/6]^2, y}}, {y, 0, 6}, PlotStyle -> {{Red,
Thickness [0. 01]}}, AxesLabel -> {"x", "y"}, Epilog -> Text["R", {-4, 3}]]
5
TITTT
4
R
3
2
-8
X
-6
-4
-2
Go with
f[x,y] = y-x+3
and calculate
S S, flex, ylaxdy
by the method of least labor on your part.

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