Problem $1$: Understanding of Discretization of Variables and Iterations

Consider the summation of the square of a continuous function $()$:

$=\text{'}|()|$

$!$

$"$

#$$\%$

where $$ is a vector of length $$ defined as a set of evenly$-$spaced values from $$ to $,$ i$.$e$.,$ in

MATLAB we define: x$=$linspace$($a$,$b$,$k$)$ and k$=1,2,3,...,$ etc