Question about finding the area of a function with delta x

I am new to this subject and I don't know what its officially called. I know that we are determining the area of a section of a graph below the graph of the function from points [a,b].

When I have a question that asks something like the area of the function 1/( x^2) on the interval 5,11 I just use my Ti-89 calculator and the 'ninc' function.

However one of my questions asks for the area on the interval 0,0.7 of delta x/(1-x^2)^(1/2). How do I figure this out exactly, this doesn't make sense to me. Shouldn't the area of the section under the function and above the x axis be the height times width with delta x representing width and the function being height? My other questions were in the format function times delta x, I don't know how to do with with delta x divided by the function.

hrm what's wrong with $$\frac {\Delta x}{\sqrt{1-x^2}}$$ ? if you take the function to be $$\frac {1}{\sqrt{1-x^2}}$$ then you have it in function * delta x form.