Notation for integration excluding endpoint

Question

I was wondering if there is there a shorter way to write

$$\lim_{x\nearrow b}\int_a^x E$$

Can one use $\int_a^{b^-}$ to denote this?

Thanks

Answer 1

You can represent what you want in this way:

$$\int_{[a,b)}f(x)\mathrm d x$$

But many times you can write for many integrals

$$\int_{[a,b)}f(x)\mathrm d x=\int_{[a,b]}f(x)\mathrm d x$$