So I was going through some questions, and these two made me curious:
1) An integrable function is always bounded
2) If a function is defined on an unbounded interval, then it cannot be integrable.
I looked through the fundamental theorem of calculus, but I just don't seem to understand the connection with the boundaries, open or closed. I did see, however, that the theorem starts with : f is continuous on an interval a,b, which I assume is bounded.
Can somebody please explain if integrable functions can indeed be UNBOUNDED?