How do I find the area under a curve between two points?

Assuming you know the equation of the line, this could possibly be done in several ways. If you are able to integrate the equation of the line definitely using your current knowledge, then do this between the two points mentioned. If you can't integrate this equation, then you can use the Trapesium Method. This means divide the area into n equal segments (splitting along the x axis). The larger the n value, the more accurate the value for the area. Then plug each x value corresponding to a divide between segments into the equation, and use the formula h/2(f(x1) + f(xn) + 2(f(x2) + ... + f(x(n-1)))) = A to find the area. Where f(xk) is the function value as the kth divide.