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.