So I'm reading through Ordinary Differential Equations by Tenenbaum and Pollard, page 76, Example 9.5, and I find it bizarre. It says that is exact on which I readily believe. It then says we can integrate each part from to , i.e. . The second integrand baffles me. The book hints that, because we're taking the integral with respect to at the point with fixed, we can therefore eliminate the . But one: Why? Two: If that's so, can't we do the same with the other one and have it be ?