Answer
$-136$
Work Step by Step
Given the values in question
$\int ^{4}_{2}x^3dx=60;$
$\int ^{4}_{2}xdx=6;$
$\int ^{4}_{2}dx=2$
$$\Rightarrow \int ^{4}_{2}\left( 10+4x-3x^{3}\right) dx=\int ^{4}_{2}10dx+\int ^{4}_{2}4xdx-\int ^{4}_{2}3x^{3}dx=10\int ^{4}_{2}dx+4\int ^{4}_{2}xdx-3\int ^{4}_{2}x^{3}dx=10\times 2+4\times 6-3\times 60=-136 $$
