This is a test of $$a\ne0$$ and $$\int_a^b e^{x^2}\,dx$$ and $(Pu)(z)= \int_\Omega K(z,w)u(w)\ dw\wedge d\bar w.$ Also testing $$\int_{-\infty}^\infty \frac{\cos x}{x^2+1}\ dx$$ and $\int_{-\infty}^\infty \frac{\cos x}{x^2+1}\ dx.$