My Question is:
Let $a$, $b \in\mathbb{R}$ with $a < b$. Define $f \colon [a, b] \to\mathbb{R}$ by $f(x) =\left\{ \begin{array}{c l} b &\mbox{ if} &x=a \\ a & \mbox{ if}&a<x≤ b. \end{array}\right.$
Use the definition of the Riemann integral to prove that $f$ is integrable on $[a, b]$ and determine the value of the integral $\int_{a}^{b} f$
I know you have to split this up into n-sub intervals but i cant really grasp the concept for this question. Any help towards the answer will be appreciated.
Hint:
Split the interval into two subintervals $$[a,b]=\Bigl[a, a+\frac1n\Bigr]\cup\Bigl[a+\frac1n,b\Bigr]$$ then use Chasles' relation.