enter image description hereI am asked to calculate the upper sum of $f(x)= 5-2x$, from $x=1$, to $x=2$ using $n$ subintervals.
Below is my working out, however, the answer is $2 + \frac1n$.
I will appreciate it if you could give me a hint, or anything. Thank you for your time.
As the function is decreasing, the upper sum comes from using the left hand endpoint of each interval. For $n$ intervals, that is $1, 1+\frac 1n, 1+\frac 2n \ldots 1+\frac {n-1}n$ The upper sum is then $\frac 1n(f(1)+f(1+\frac 1n)+f(1+\frac 2n)+\ldots f(1+\frac {n-1}n))$ That is an arithmetic series which you should be able to sum.