Since $\int x^{k}\mathrm{d}x=\frac{x^{k+1}}{k+1}$ for $k\neq -1$, replace $\int x\mathrm{d}x$ with $\frac{x^{2}}{2}$. Multiply $\frac{5}{6}$ times $\frac{x^{2}}{2}$.
$$\frac{5x^{2}}{12}+\int -6\mathrm{d}x$$
Find the integral of $-6$ using the table of common integrals rule $\int a\mathrm{d}x=ax$.
$$\frac{5x^{2}}{12}-6x$$
The definite integral is the antiderivative of the expression evaluated at the upper limit of integration minus the antiderivative evaluated at the lower limit of integration.
