The following function is defined over the interval [-L, L]:

f(x) = px4 + qx5.

If it is expressed as a Fourier series, 

$\rm f(x)=a_0 +\displaystyle\sum^\infty_{n=1} \left\{a_n \sin\left( \frac{\pi x}{L} \right) +b_n\cos\left( \frac{\pi x}{L} \right) \right\} $,

which options amongst the following are true?

A function f(x), that is smooth and convex-shaped between interval (x_l , s_u) is shown in the figure. This function is observed at odd number of regularly spaced points. If the area under the function is computed numerically, then .