In a definite integral, as we allowed to use the same symbol in the upper/lower bound of the integration as the variable of the integrated function?

Question

Occassionally I see the notation $$\int_{0}^{x^2}\sin x\mathrm{d}x$$ and some author will avoid using $x$ as the variable of the integrated function by writting $$\int_{0}^{x^2}\sin t\mathrm{d}t.$$

My question is, is there anything wrong with writing $\int_{0}^{x^2}\sin x\mathrm{d}x$？

Answer 1

It is advisable to write \begin{align*} \int_{g(x)}^{h(x)}f(t)\mathrm{d}t \end{align*} This is because $t$ represents the variable of integration and the pair $g(x)$ and $h(x)$ indicates the limits of integration.