Fundamental Theorem of Calculus

[Jason76]

Determine the intervals on which the Fundamental theorem of Calculus could be used for \(\displaystyle f(x) = \dfrac{1}{x - 4}\) Explain in complete sentences what conditions must be met to use this theorem?

Any starting hint?

 

[daon2]

Any starting hint?

What is the statement of the fundamental theorem of calculus? On what intervals might the "If" part of the theorem not hold?

 

[Jason76]

It seems the answer (based on looking at a similar problem) would be any interval not containing \(\displaystyle 4\) and so the intervals would be: \(\displaystyle (-\infty, 4)\) Union sign \(\displaystyle (4, \infty)\)

But I don't know the reasoning of why. I can see that 4 came finding a discontinutiy in the function (setting the denominator = 0 and solving for x).