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I need help desperately with this question, it's really tricky! I drew it up so it'd be easier to read, since typing all those parenthesis can be confusing.

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Thank you for your help!

Since all of the integrals are from 3 down to -1, that means we can split them apart.

That is, using upper case I for integral, we have I[2g(x) - 4f(x)]dx.

This can be made into the difference of two integrals, as I[2g(x)]dx - I[4f(x)]dx.

A constant can be factored outside of each integral, giving 2{I[g(x)]dx} - 4{I[f(x)]dx}.

Since I[g(x)]dx = A and I[f(x)]dx = B, these values can be put in.

This gives 2{A} - 4{B} = 2A - 4B.

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