Numerical Integration and Differentiation

In calculus analytical methods exist to find the derivative and definite integral of a given function $y=f(x)$, if the expression of $f(x)$ is available and it is not complicated. However, when $f(x)$ is not a simple function, or it is given as a set of $n+1$ discrete points $f(x_0),\cdots,f(x_n)$, numerical methods need to be used to estimate its derivative and integral.