I am trying to set up and evaluate the definite integral that gives the area of the region bounded by the graph of the function $\displaystyle y = x ^3 -2x$ and the tangent line to the graph at the point ( -1, 1)

Now, i am aware this is an area problem so i probably have

$\displaystyle a = \int f(x) - g(x) dx$

would g(x) = x ^3 -2x ?

for the tangent line would it be in the form y = mx + b?

How would i find that? I have graphed the x ^3 -2x and made the point ( -1, 1) and can see the region for the area.

Would i need to take the dirivitive of x ^3 -2x and plug in -1 for x?

$\displaystyle x ^3 -2x = 3(-1)^2 - 2 = 1 $