I'm hoping I can get some help with the following question: Does definite integration (from x = 0 to x = 1) of functions in Pn correspond to some linear transformation from Rn+1 to R? OK, well my original answer was yes, but the textbook says "no, except for P0" which I do not understand. So I have p(x) = anxn + an-1xn-1 + ... + a1x + a0 If I integrate from 0 to 1, I get: P(1) = an/(n+1) + an-1/n + ... + a1/2 + a0 Right? So I have T(an, an-1, ..., a1, a0) = (an/(n+1) + an-1/n + ... + a1/2 + a0) and T: Rn+1 -> R And if I want to show that it is linear, then I show that the transformation has these properties: T(kx) = kT(x) and T(x+y) = T(x) + T(y) and I think both cases are obvious. And T is multiplication by [1/(n+1) | 1/n . . . 1/2 | 1] What am I missing? Thanks in advance for any help.