Prove that the piecewise function f(x) = 1 , if x =1/2 and f(x) = 0, otherwise is integrable on the interval [0, 1] using the Darboux Method.

I understand that the integral from x = 0 to x = 1/2 will evaluate to 0 and the integral from x = 1/2 to x = 1 also evaluates to 0.

But how can I show this more formally? The issue arises at x = 1/2, how do I deal with that if using Darboux upper and lower integrals?