This is a question ($12$) from apostol calculus $1$ execise on alternate definition of integral.
Here the integral refers to integral of step function, $[x_k,x_{k-1}]$ are partitions and $s_k$ is function value in these interval.
The answer given is $A,B,C$ but I found answer as $A,C$. How is $B$ correct? I think as partitions of $s$ and $t$ in option $(b)$ may not be identical, so answer would not be same.