I'm still wondering though how to arrive at the result....
The only way I can think of, is calculating the integrals of (1+x) with 1 and with cosx (after norming them) to find the projection, which is (1+pi).
And then calculate the integral of ((1+x)-(1+pi))^2, which is indeed .
But isn't this analysis and calculus?
Is there an easier way?