Solving Improper Integrals: Do First Two Equal Third?

[kingwinner]

Homework Statement

-∞
∫f(t)dt
a

b
∫f(t)dt
-∞

b
∫f(t)dt
a

Now add the first two integrals, do we get the third integral?

Homework Equations

N/A

The Attempt at a Solution

Suppose we have

c
∫f(t)dt
a

b
∫f(t)dt
c

b
∫f(t)dt
a

Then adding the first two integrals will give the third integral, but what happens in the case of improper integrals?

 

[sutupidmath]

this would hold, i assume, if
-∞
∫f(t)dt
a

b
∫f(t)dt
-∞


would converge.

 

[kingwinner]

So the property

holds also for improper integrals?