A Property of Definite Integral

[Abdul Quadeer]

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

http://latex.codecogs.com/gif.latex?\int_{a}^{b}f(x)dx&space;=&space;\int_{a}^{c_{1}}f(x )dx&space;+&space;\int_{c_{1}}^{c_{2}}f(x)dx&space;+&space;......\int_{c_{ n}}^{b}f(x)dx&space;\\\\&space;\textup{such&space;that}&space;\&space;c_{1},&space;c_{ 2}......c_{n}\notin&space;[a,b]

[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!

[Abdul Quadeer]

Thanks!