# Proving the second fundamental theorem of calculus?

1. Jan 10, 2017

### Vitani11

1. The problem statement, all variables and given/known data
Show that Dx∫f(u)du = f(x) Where the integral is evaluated from a to x. (Hint: Do Taylor expansion of f(u) around x).

2. Relevant equations
None

3. The attempt at a solution
I have

... = Dx(F(u)+C) = Dx(F(x-a)+C) = dxF(x) - dxF(a) = f(x)-f(a). My problem is that it should be only f(x), not f(x) - f(a). I did a taylor expansion of f(u) around x and I'm not sure how that is supposed to help me...

2. Jan 10, 2017

### Vitani11

I know that for an integral F(a) (where a is not a variable) the derivative of the integral would be 0, and that's why it would not be included in the final answer, but I don't know how to show that.

3. Jan 10, 2017

### haruspex

You are starting with $\int_a^xf(u)du$, so that is a function of x (or maybe of a and x). It is not a function of u.