The graph of a function $f(x)$ is given below. $($Each grid square is $1$ unit wide and $1$ unit high.$)$

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Use rectangles to estimate the area under the curve on the interval. $($Determine the number of rectangles, the width of the rectangles in each case, and which sample points should be used in your calculation using the given directions. When determining the height of a rectangle, assume that the height is a multiple of $0\mathrm{.}5.)$

$($a$)$ On the interval $0,12$ using $4$ subintervals of equal width and right endpoints as sample points. square units

$($b$)$ On the interval $0,12$ using $12$ subintervals of equal width and right endpoints as sample points. square units

$($c$)$ On the interval $0,12$ using $6$ subintervals of equal width and midpoints as sample points. square units