$(18$pts$)$ Find the total area between the region $-1x1$ on the $x-$axis and the graph of $f(x)=4x^3-4x.$

a$)$ Identify the zeros of $f$ :

b$)$ Subdivide the interval $-1,1$ at the zeros of $f$ :

c$)$ Integrate over each subinterval:

d$)$ Add the absolute values of the integrals to obtain the total area: