Along with giving us a technique to compute antiderivatives, integration by parts is very important theoretically. In this context, it can be thought of as a technique for moving derivatives off of one function and onto another. To see what we mean, suppose that f(x) andg(x) are functions with f(0) = g(0) = 0, f(1) = g(1) = 0 and with continuous second derivatives f''(x)and g''(x). Use integration by parts twice to show that the integral from [0,1] of f''(x)g(x) dx = the integral from [0,1] of f(x)g''(x) dx.