I'm using a textbook in my Advanced Calculus class that might have funny notation for an integral. I couldn't figure out how to type it, so I snipped a picture of it and am attaching it:
I can't tell if the integral simply has a minus sign for the "a" bound of integration, or if it's something I haven't seen before. I tried using context clues in my textbook, but honestly it's not my favorite one and is not very clear a lot of the time. If anyone knows what this means, I'd appreciate it!
Best Answer
The notation$$\underline{\int}_a^bf$$has no minus sign; instead, the $\int$ is underlined there. It denotes the supremum of all lower sums of $f$ with respect of all partitions of $[a,b]$. Another notation used here for the same purpose is$$\underline\sum(f,P).$$