Evaluate each of the following integrals as the limit of sums:

f(x) is continuous in [a,b]

here h=(b-a)/n


S=cos(a)+ cos(a+h)+ cos(a+2h)+ cos(a+3h)+…………………..+ cos(a+(n-1)h)
Putting h=(b-a)/n

As we know
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Which is trigonometry formula of sin(b)-sin(a)
Final answer is sin(b)-sin(a)
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