Answer
$=0.164$ square units
Work Step by Step
We know that:
$f(x)=x^2+3x+1$
We can use this to find the height of the rectangle by plugging in the left $x$ value, $0.2$:
$height=f(0.2)=0.2^{2}+3(0.2)+1$
$=0.04+0.6+1$
$=1.64$
Thus the height of the rectangle is 1.64.
The base of the rectangle is the difference in $x$ values from left to right:
$base=0.3-0.2$
$=0.1$
Thus the area is:
$Area=base*height$
$=0.1*1.64$
$=0.164$ square units