Chapter 4 - Integrals - 4.4 Indefinite Integrals and the Net Change Theorem - 4.4 Exercises - Page 336: 20

$11$

First we evaluate the integrand $\int 4x^3 - 3x^2 + 2x dx $, which is $ x^4 -x^3 + x^2 $ We then substitute the bounds of integration $1$ and $2$ and get $(2^4 - 2^3 + 2^2) - (1^4 - 1^3 + 1^2) = (16 - 8 + 4) - (1 - 1 + 1) = (12) - (1) = 11 $