Answer
$4$
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 $\displaystyle \Delta x=\frac{b-a}{n}$
Now,
$\text{Left Riemann sum}=(0+0.5+1+1.5) =3$ and $\text{Right Riemann sum}=(0.5+1+1.5+2) =5$
This gives: $Average=\dfrac{3+5}{2}=4$
Therefore, the total change of $f(t)$ $=\int_2^6 f'(t) \ dt=4$
