Approaching a Definite Integral with Undefined Limits

[Apteronotus]

I want to find the area under a function $$f$$ in the interval $$(a,b)$$.

I've calculated the integral of the function $$f$$, and its given by:
$$\int f(x) dx=F(x)$$

Now the problem I have is that $$F(a)$$ is not defined. In particular, $$F(x)=\frac{h(x)}{g(x)}$$ and
as $$x \rightarrow a, h(x) \rightarrow 0$$
and $$x \rightarrow a, g(x) \rightarrow 0$$

How would I approach this problem?

 

[NoMoreExams]

Look up improper integrals? (http://en.wikipedia.org/wiki/Improper_integrals)

 

[Apteronotus]

Yes of course!
Thank you kindly NME.

 

[prav]

You can probably use the L'Hospital's rule if everything is good since this is 0/0.
Look up Bender and Orszag maybe.

 

[Apteronotus]

Thanks for the helpful tip prav.