Calculus question

Question

Suppose the integral from 1 to 6 g(x)dx=10 and the integral from 4 to 6 g(x)dx=-2 , find the value of the integral from 1 to 4 2g(x)dx. I have tried solving this problem but cannot and everyone else asking this type of question hasn’t gotten a quality explanation.

Answer 1

[int from 1 to 6 of g(x) dx] = [int from 1 to 4 of g(x)dx] + [integral from 4 to 6 of g(x)dx]

There are three integrals, they are all in between [ ]

The 1st integral = 10 (given) and the 3rd integral is given as -2.

Since 10 = 12 + (-2) it follows that the 2nd integral is 12.

That is int from 1 to 4 of g(x)dx = 12, so int from 1 to 4 of 2g(x)dx = 2[int from 1 to 4 of g(x)dx] = 2*12 = 24