Solving a limit problem using Riemann Sum

A limit problem where Riemann sum is converted to definite integral.

[shailabchapagain]

wow !Thankyou so much sir for such a usefull video #highlyappreciated

[ckjain_maths]

Sir,
I have seen many videos regarding changing of Riemann sum to definite integral. But I could not grasp a clear- cut and standard method. The procedure is dependent on estimation and speculation.
Please, comment on my observation.

[ckjain_maths]

Conversion of a definite integral to Riemann sum is simple and procedural. But converting a Riemann sum into integral is based on speculations and approximations.It does require determination of upper limit, lower limit and the integrand function. I have not come across a clear cut procedure.