The upper sum of the integral

`int_a^b f(t)dt`

is

`U=sum_{i=0}^{n-1} f(x^+) Delta x` where `Delta x = {b-a}/n` , `f(x^+)=max(f)` on the interval `[x_i,x_{i+1}]` and `x_i=a+i Delta x`

The lower sum is

`L=sum_{i=0}^{n-1} f(x^-) Delta x` where `f(x^-)=min(f)` on the same interval

Since `f(x)=2+sin x` , and the bounds on the...

(The entire section contains 200 words.)

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