Why I didn't major in math

[Dr Aum]

But then I thought differentiation under the intergration sign was silly...

Differentiation? Do you mean derivative?

Integrals of derivatives are useful because of that F(b)-F(a) theorem (I forget what it's called).

Nope, I mean differentiation under the integral sign. (Apparently its an easier method of solving complex integrals by differentiating the integrand with respect to a new variable and then integrating that with respect to the original variable, as opposed to integration by parts.)

Oops, my mistake. I just learned on Wikipedia that differentiation is the same as what I was taught as "taking the derivative of." Suddenly differential equations make much more sense.