What is analytical fn?Is definite integral is same as Riemannintegral?

Answer 1

An analytic function is a function which is infinitely differentiable. Examples are polynomials, exponentials, etc. Analytical functions are smooth, have no holes, jumps and similarly for their differentials.

A definite integral is an integral taken between two boundaries. It corresponds so to say to the surface between y=0 and y=f(x), between a certain x=a and x=b.

Mathematically definite integrals can be defined in several ways. The definition according to Riemann is called the Riemann integral.
But there are other possible definitions like for instance the Lebesque integral and the Henstock-Kurzweil integral.