# Newton Leibnitz Formula for Evaluating Definite Integrals

1. Mar 3, 2015

### andyrk

Lately, I have been trying really hard to understand the Newton Leibnitz Formula for evaluating Definite Integrals. It states that-
If f(x) is continuous in [a,b] then $\int_a^b f(x) dx = F(b) - F(a)$.
But one thing that just doesn't make sense to me is that why should f(x) be continuous in [a,b] if we need to apply this formula?

Last edited: Mar 3, 2015
2. Mar 3, 2015

### andyrk

Anybody there?

3. Mar 3, 2015

### AURUM

do you know limit as as sum formula?

4. Mar 3, 2015

### HallsofIvy

It doesn't say that. The statement "if a then b" means "if a is true then b is true". It does NOT say anything about what happens if the hypothesis is NOT true.

This theorem says that "if f is continuous on the interval [a, b], then $\int_a^b f(t)dt= F(b)- F(a)$". It does NOT say anything about what happens if f is NOT continuous, If f is not continuous, then this may or may not be true.

5. Mar 3, 2015

6. Mar 4, 2015