I was trying to learn Riemann integration. So after that I wanted to practice some questions and got this.
Given a function, $f(x) = \sin{x}\ \ \text{if}\ \ x = \frac{1}{n}$ and $f(x) = \cos{x} \ \text{ otherwise} $.
Check if it is integrable.Now I was reading the solution and found that they have written "Note that f has only finite discontinuities in $[\frac{1}{N}, 1]$ .Hence integrable in $[\frac{1}{N}, 1]$". I have found this in a lot of similar problems but couldn't figure out the reason. Can anyone tell me how it works?
I am finding difficulty with the part where there are only a finite discontinuities in the interval. I don't understand the logic behind it.