# Filling the Area Under a Curve Bounded on the Left and Right

Grandson & I are once again using Mathematica to demonstrate some of his calculus. He's on definite integrals now. His problem asked him to determine the area under the curve for y = 3 x, bounded by x = 1 & x = 5. We easily solved the problem using Integrate but he asked what this looked like when plotted. I first showed him on paper..., no, that wasn't enough, "How do we do this in MM?, he asked. (We came up with a solution which I'll provide as an answer below but obviously, welcome other thoughts, improvements, etc.)

Here's our solution:

y[x_]:=3 x
xNegPlotRange = -1; xPosPlotRange = 6; yNegPlotRange = -1; \
yPosPlotRange = 20;
strPlotLabel1 = "Area Under a Curve
Curve Described by: y = 3 x (Green Line),
Bounded by x = 1 (Left, Red) & X = 5 (Right, Blue)";
p1 = Plot[y[x], {x, 1, 5}, Axes -> True, Filling -> Axis,
FillingStyle -> Green, Frame -> False, AxesLabel -> {"x", "y"},
PlotLabel -> strPlotLabel1,
AxesStyle -> Directive[Bold, Medium, Arrowheads[{0, 0.05}]],
PlotLegends -> "AllExpressions",
PlotRange -> {{xNegPlotRange, xPosPlotRange}, {yNegPlotRange,
yPosPlotRange}}];
p2 = Plot[100 Sign[x - 1], {x, -10, 10}, ExclusionsStyle -> Red,
PlotRange -> {-10, 20}];
p3 = Plot[100 Sign[x - 5], {x, -10, 10}, ExclusionsStyle -> Blue,
PlotRange -> {-10, 20}];
Show[p1, p2, p3,
PlotRange -> {{xNegPlotRange, xPosPlotRange}, {yNegPlotRange,
yPosPlotRange}}] Suggestions?