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Regarding the following sum and integration:

enter image description here

I don't understand the difference between t and 𝛕.

When nΔ𝛕 goes to zero the text says it becomes 𝛕. But why not t. Aren't an arbitrary point t and 𝛕 the same? I don't have such confusion with an integral such as f(x) = integral 3x dx or here.

But the equation in my question has both t and 𝛕 makes me very confused.

I'm missing something fundamental here but stuck with seeing the difference. How can we grasp the difference?

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    $\begingroup$ $t$ is a fixed number throughout all of the above. $\endgroup$ – copper.hat Sep 18 '19 at 13:14
  • $\begingroup$ Which book/ what kind of book is this? The limit for $\Delta \tau$ seems very strange as the limit still contains the $\Delta \tau$ that is supposed to be zero. $\endgroup$ – quarague Sep 18 '19 at 13:47

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