Answer
$0.25$
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,
$\text{Left Riemann sum}=[0.5+0+0+(-0.5)+0+0] =0$ and $\text{Right Riemann sum}=[1+0.5+(-0.5)+0+0+(-0.5)]+1 =0.5$
This gives: $Average=\dfrac{0.5+0}{2}=0.25$
Therefore, the total change of $f(t)$ $=\int_{-1}^2 f'(t) \ dt=0.25$
