$($#$6)$ approximate the area under $f(x)=10x-x^2,$ above the $x-$axis, on $1,7$ with $n=6$ rectangles using the left and right endpoint, trapezoidal rule $($av$.$ of l$.$e$.$ & r$.$e$.)$ and midpoint methods $($include summation notation and endpoint values$)$ and then find the exact area using a definite integral $($include a graph with shaded region$)$