Question

How to solve this additional mathematics question ?

Answer 1

We can use some funky properties of integrals here to express the integral in terms of ones we already know. Note that,
$\int^4_1{[3f(x)+2]}dx = 3\int^4_1f(x) dx + \int2dx$ then,
$=(3 \times 10) + \int^4_1{2}dx$, since we know the value of $\int^4_1f(x)_$.

I will leave you to complete the remaining, easy steps.