Answer
6
Work Step by Step
The interval [a,b] is subdivided into n intervals,
f is a continuous function over [a,b],
Left Riemann sum $=\displaystyle \sum_{k=0}^{n-1}f(x_{k})\Delta x$
$=[f(x_{0})+f(x_{1})+\cdots+f(x_{n-1})]\Delta x$,
where $a=x_{0} < x_{1} < \cdots < x_{n}=b$
are the endpoints of the subdivisions,
and $\displaystyle \Delta x=\frac{b-a}{n}$.
-----------------
$f(x)=x^{2},\ \ [a,b]=[-2,2],\ \ n=4$
$\displaystyle \Delta x=\frac{b-a}{n}=\frac{2-(-2)}{4}=1$
$\left[\begin{array}{llllll}
k & 0 & 1 & 2 & 3 & 4\\
x_{k} & -2 & -1 & 0 & 1 & 2\\
f(x_{k}) & 4 & 1 & 0 & 1 & ..
\end{array}\right]$
Left Riemann sum $=(4+1+0+1)\cdot 1$
$=6\cdot 1=6$
