Confusion with variables in the summation and integration

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Regarding the following sum and integration:

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I don't understand the difference between t and .

When nΔ goes to zero the text says it becomes . But why not t. Aren't an arbitrary point t and 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 makes me very confused.

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