Answer
$15.76 \ L$
Work Step by Step
The interval $[a,b]$ is subdivided into $n$ intervals, and the function
$f(x)$ is a continuous function over $[a,b]$.
Here, 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 $\displaystyle \Delta x=\frac{b-a}{n}$
We are given that $r(t)=3t^2+5 \ L/min$ and $n=5$
$\displaystyle \Delta x=\frac{2-0}{5}=0.4$ with interval $[0,2]$
Therefore, $\int_0^2 r(t) \ dt=[r(0)+r(0.4)+r(0.8)+r(1.2)+r(1.6)] \times 0.4\\=(5+5.48+6.92+9.32+12.68) \times 0.4 \\=15.76 \ L$
