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## Homework Statement

This isn't a specific problem ;)

## Homework Equations

## The Attempt at a Solution

My thought process, skip to the last paragraph if you want the question:

I was wondering how you compute an integral at a specific x value, lets say c. Based on the fact that the integral is a function, my very first thought was that I should treat it like any other function and just "plug c into" the integral like -

If [itex]F(x)[/itex] is the integral and [itex]f(x)[/itex] is the function you're integrating,

[tex]\int{f(c)}=F(c)[/tex]

Then I thought that you can't treat the integral like any other function because [itex]F(c)[/itex] actually represents the sum of the values of [itex]f(x)[/itex] from x=0 to x=c, and therefore the proper way to do this would be to evaluate a definite integral from 0 to c. I don't know if there's a flaw in my thinking so I've included it.

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Question: If I want to compute an integral at x=c, should I calculate the definite integral from x=0 to x=c?

Example:

[tex]\int_{0}^{c} cos(x) dx = \left[ sin(x) \right]_{0}^{c} = sin(c) -sin(0) = sin(c)[/tex]

I have this follow-up question, but first I want to see if this is right.

**Thanks!**(And if there's a better way to use LaTeX, please tell me, I'm clueless :D)

Similarly- sorry if the way I'm expressing the math is wrong, if so please correct me.