$\int_2^4 x^5 \: dx = \left[ \fracx^66 \right]_2^4 = \frac4^66 - \frac2^66 = 672$
$\int_2^4 (3x^2-5x+6) \: dx= \left[ \frac3x^33-\frac5x^22+6x \right]_2^4 =$ $\left( 4^3-\frac5 \cdot 4^22+6\cdot4 \right) - \left(2^3-\frac5\cdot 2^22+6 \cdot 2 \right) =$ $(64-40+24) - (8-10+12) = 48-10=38$ (…)