How to solve integrals given a set

4 integrals are given:

1. Integral from 0 to 100 of f(x) dx = 9
2. Integral from 0 to 35 of f(x) dx = -4
3. Integral from 0 to 100 of g(x) dx = -1
4. Integral from 35 to 100 of g(x) dx = 21

How do you find the integral from 0 to 35 of [(1/5)g(x) - 3f(x)] dx?

∫(g(x)/5 - 3f(x))dx [0,35]
= (1/5)∫(g(x)dx [0,35]) - 3∫(f(x)dx [0,35])
= (1/5)(∫(g(x)dx [0,100]) - ∫(g(x)dx [35,100])) - 3(-4)
= (1/5)(-1 - 21) + 12
= (1/5)(-22) + 12
= (-22 + 60)/5
= 38/5