For this problem, you will need to use the Desmos Riemann Sum Calculator. (This link opens a new tab/window.)

Initially, the calculator shows a left Riemann sum with $n=5$ subintervals for the function $f(x)=2x+1$ on the interval $[1,4]$. Use the applet to compute the following sums for this function on this interval.
$L_5 =$ , $M_5 =$ , $R_5 =$
$L_{25} =$ , $M_{25} =$ , $R_{25} =$
$L_{100} =$ , $M_{100} =$ , $R_{100} =$

Now use basic geometry to determine the exact area bounded by $f(x)=2x+1$ and the $x$-axis on the interval $[1,4]$.
Exact Area =

Make a note of any patterns you observe.

You can earn partial credit on this problem.