Step 1 :The integral of a function from a to b is the area under the curve of the function from a to b. The integral of \(3f(x)\) from -2 to 7 is given as 12. This means that the integral of \(f(x)\) from -2 to 7 is \(12/3 = 4\).
Step 2 :The integral of \(f(x)\) from 5 to 7 is given as 2.
Step 3 :To find the integral of \(f(x)\) from -2 to 5, we can subtract the integral of \(f(x)\) from 5 to 7 from the integral of \(f(x)\) from -2 to 7.
Step 4 :Subtracting, we get \(4 - 2 = 2\).
Step 5 :Final Answer: The integral of \(f(x)\) from -2 to 5 is \(\boxed{2}\).