Hi all,

I want to know how to plot the partitions and the trapezoids when I have the input of the function only and the number of interval? This is the images that I want to achieve

I have this code for starter, but have no idea to convert it to Trapezoidal rule and to Simpson’s rule:

```
using Plots, LaTeXStrings, ValidatedNumerics, Plots.PlotMeasures
gr()
f(x) = 3x^2 + x + 1
function make_intervals(N=10)
xs = range(-1, stop=1, length=N+1)
return [xs[i]..xs[i+1] for i in 1:length(xs)-1]
end
# Plot Riemann Sums
intervals = make_intervals(10)
p = plot(aspect_ratio=:equal)
for X in intervals
Y = f(X)
plot!(IntervalBox(X, Interval(0, Y.hi)), c=:blue, label="", alpha=0.1)
end
plot!(f, -1, 1, xtick=-1:1:1, xlims=(-1,1),label=L"3x^2 + x + 1",
bottom_margin=5mm)
annotate!([(-0.9,-0.07, (L"x_{0}", 6, :black))])
annotate!([(-0.7,-0.07, (L"x_{1}", 6, :black))])
annotate!([(-0.5,-0.07, (L"x_{2}", 6, :black))])
annotate!([(0,-0.07, (L"\dots", 6, :black))])
annotate!([(0.77,-0.07, (L"x_{n-1}", 6, :black))])
annotate!([(1.07,-0.07, (L"x_{n}", 6, :black))])
```