What is an example of a definite integral satisfying this property?

[zorro]

Can somebody give me an example of a definite integral satisfying this property? :

 

[Mark44]

$$\int_1^2 x~dx = 3/2$$
Let c₁ = -1, and c₂ = -2

Compare the first integral with
$$\int_1^{-1} x~dx + \int_{-1}^{-2} x~dx + \int_{-2}^{2} x~dx$$

What do you get?

 

[HallsofIvy]

That's true for any integral as long as the integrand is integrable over all those intervals!

 

[zorro]

Thanks!