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Yes, there are other ways to write the limit expression involving the integral. Here are some alternative notations:

1. Using the definition of the integral:

$$\underset{ℎ\to 0}{\lim }{\int }_{𝑥}^{𝑥+ℎ}𝑓(𝑡)𝑑𝑡$$

2. Using a different variable for the limit:

$$\underset{𝜖\to 0}{\lim }{\int }_{𝑥}^{𝑥+𝜖}𝑓(𝑡)𝑑𝑡$$

3. Expressing the integral in terms of a differential:

$$\underset{ℎ\to 0}{\lim }{\int }_{𝑥}^{𝑥+ℎ}𝑓(𝑡)𝑑𝑡=\frac{𝑑}{𝑑𝑥}{\int }_{𝑎}^{𝑥}𝑓(𝑡)𝑑𝑡\text{(if the integral is from a fixed lower limit }𝑎\text{)}$$

4. Using the concept of the Fundamental Theorem of Calculus:

$$\underset{ℎ\to 0}{\lim }\frac{1}{ℎ}{\int }_{𝑥}^{𝑥+ℎ}𝑓(𝑡)𝑑𝑡=𝑓(𝑥)\text{(this follows from the Mean Value Theorem for Integrals)}$$

These notations express the same concept, which is the behavior of the definite integral as the upper limit approaches the lower limit. The use of different symbols or approaches may depend on the context or preference in notation.