c$)$ A topic we will study later in this course is the total change of a function. It states that if $f(x)$ is a function that describes the rate of change of a quantity, then the total change in the quantity over an interval $a,b$ is the area bounded by $f(x),$ the $x-$axis, and the vertical lines $x=$a and $x=b.$ Since the functions given in this problem describe the number of new cases per day $($the rate of change of cases$),$ the area under these curves represents the cumulative total cases over a given interval. Both functions $A(t)$ and $B(t)$ are graphed below.

The area of each shaded region is approximately $400,000.$ What does this mean in the context of the problem? Is either country doing better than the other?