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## Main Question or Discussion Point

While doing work, I always see notation like:

F(x) = ∫

F(x) = ∫

What is the exact reasoning we always use the upper limit? What is the lower limit was a variable? From FTC 2, the answer for the first equation is F(x) - F(0) right yet is written as F(x) when F(0) has a value? An explanation would be very helpful.

How would this be assessed: F(x) = ∫

From examples, I see that taking the derivative of [1] requires that you apply chain rule, so that you end up multiplying the derivative of this by 2x, in this example, since that is the derivative of the variable introduced with respect to the original variable. I'm just slightly confused on how we would assess this function when not taking the derivative and if someone could provide the general answer for a function in this form:

F(x) = ∫

with an explanation that would be great! Thank you so much! :)

F(x) = ∫

_{0}^{x}f(t)dt - first equationF(x) = ∫

_{1}^{x}f(t)dtWhat is the exact reasoning we always use the upper limit? What is the lower limit was a variable? From FTC 2, the answer for the first equation is F(x) - F(0) right yet is written as F(x) when F(0) has a value? An explanation would be very helpful.

How would this be assessed: F(x) = ∫

_{0}^{x2}f(t)dt [1] ?From examples, I see that taking the derivative of [1] requires that you apply chain rule, so that you end up multiplying the derivative of this by 2x, in this example, since that is the derivative of the variable introduced with respect to the original variable. I'm just slightly confused on how we would assess this function when not taking the derivative and if someone could provide the general answer for a function in this form:

F(x) = ∫

_{g(x)}^{f(x)}f(t)dtwith an explanation that would be great! Thank you so much! :)