Integrals

Hi /sci/

I'm having orals for a french computer engineering school (i'm french). Amongst those orals, there is a maths oral. The thing is, we didn't study integrals in class yet. And the book is f*** stupid. So could anybody clearly explain to me what integrals are, how they work, etc.

Thanks a lot ;)

I am looking for the antiderivative to
f(x)=exp(-sqrt(x^2+a))
Does anyone know about a good resource to get this? My ass old version of derive fails at this.