Evaluate: `int_a^bsinx dx` using limit of sum

Explanation

Here lower limit `=a`, and
upper limit `=b,f(x)=sinx`

Now, By definition

`f(A+ih)=f(a+ih)=sin(a+ih)`

f is continuous on (a,b) and vwe divide (a,b) into n sub-intervals of equal length.

`h=(b−a)/n​`

`∴nh=b−a`

Also as `n→∞,h→0`

`∫_a^b​sinxdx=lim_(h→0​)∑_(i=1)^n​f(a+ih)`

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