The correct answer is A) 20.
To find the definite integral:
$$(4x^3 - 3x^2 + 4x + 2)dx$$
We must first expand the given function.
(4x^3 - 3x^2 + 4x + 2)dx = 4x^3 + 2dx
Then, we can evaluate the integral as follows:
$$\int4x^3dx = 4\int(x^3dx) = 4x^4+C$$