If $\int_0^2 f(x)\,dx = 3$, what is $\int_0^2 \left(2f(x) + 1\right)dx$?

Explanation

1. 01

   Split: $2\int_0^2 f(x)\,dx + \int_0^2 1\,dx = 2 \times 3 + 2$.

2. 02

   That is 8.