First thing I would recommend is to use specific values for a, b, c to get an idea of what is going on. The following graph has sliders for a,b,c so you can adjust them to get different pictures:
Notice that line 3 the equation is solved for y2. Then functions are defined for the +/- square root. Line 9 shows an integral for finding the area under the curve. Note that f(x) is not actually defined at b2/c (improper integral). Not sure what the expectation is for you to find the anti-derivative of f(x). Wolfram Alpha shows it to be a long involved process.