Some functions that would be fun to integrate on (0, π].

y=[x*[1-x/pi]]^2

Analytic except at the endpoint, where it is C2. Integral can be done analytically.

y=1+cos([pi*cos(x)])

Analytic, infinite Fourier series, but the integral can't be done analytically.

y=sin(x)^4

Analytic, finite Fourier series, and the integral can be done analytically.

y=exp([-cos(2*x)])

Analytic, infinite Fourier series, but the integral cannot be done analytically

y=1/(2+cos(2*x))

Analytic, infinite Fourier series, integral can be done analytically.


Graph of the formula

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