Let function $f$ be defined, such that $f(x)=1$ for irrational $x$ and $f(x)=2$ for rational $x$. Compute $\int_0^1 f(x)\,dx$.
How would I even???? Would it just be $1$ because there are infinitely many irrational numbers between each rational number or ?????????
I don't even know where to start with this.