Problem $3.$ a$.)$ Sketch a graph of $f(x)=x^2$ on $a,b,$ where ${\displaystyle \underset{a}{\overset{b}{}}}{x}^{2}dx{\displaystyle \underset{a}{\overset{b}{}}}{x}^{2}dx=\underset{n}{lim}{\displaystyle \underset{k=1}{\overset{n}{}}}f(x_k)x0.$ Interpret ${\displaystyle \underset{a}{\overset{b}{}}}{x}^{2}dx$ geometrically$-$that $is,$ sketch the integral.

$b.$