Integrating with unknown method

[AnnieF]

Homework Statement

If (the integral from -3 to 2)f(x)dx=-1, (the integral from -1 to 5)f(x)dx=8, and (the integral from -3 to 5) f(x)dx=6, then (the integral from -1 to 2)f(x)dx= ?

Homework Equations

This is the part I'm struggling with.

The Attempt at a Solution

I know that the answer is as follows:

Note that (the integral from -3 to -1) f(x)dx= (the integral from -3 to 5)f(x)dx- (the integral from -1 to 5) f(x)dx= 6-8= -2. So (the integral from -1 to 2) f(x)dx= (the integral from -3 to 2) f(x)dx- (the integral from -3 to -1) f(x)dx= -1-(-2)= 1

I just don't understand what rule allows you to do the above.

 

[SammyS]

Homework Statement

If (the integral from -3 to 2)f(x)dx=-1, (the integral from -1 to 5)f(x)dx=8, and (the integral from -3 to 5) f(x)dx=6, then (the integral from -1 to 2)f(x)dx= ?

Homework Equations

This is the part I'm struggling with.

The Attempt at a Solution

I know that the answer is as follows:

Note that (the integral from -3 to -1) f(x)dx= (the integral from -3 to 5)f(x)dx- (the integral from -1 to 5) f(x)dx= 6-8= -2. So (the integral from -1 to 2) f(x)dx= (the integral from -3 to 2) f(x)dx- (the integral from -3 to -1) f(x)dx= -1-(-2)= 1

I just don't understand what rule allows you to do the above.

How does the integral from -3 to -1 plus the integral from -1 to 2 plus the integral from 2 to 5 , compare to the integral from -3 to 5 ?