Consider the function $f(x)=|4x-2|$ on the interval $-1,1.$

$($a$)$ Sketch a graph of $f$ below and shade the area between the curve and the $x-$axis on the interval. $$

$($b$)$ Approximate the area of the shaded region with $6$ rectangles and left endpoints. Draw the approximating rectangles in the graph above.

$($c$)$ List three different methods for finding the area of the region exactly. Use one of the methods to find the area.