What are the algos for differentiating and integrating functions?

There is a whole discipline in this matter. You should look for numerical analysys (http://en.wikipedia.org/wiki/Numerical_analysis).

Start with this and you can make algos to resolve the problems.

Are you talking about numerical or symbolic differentiation/integration? If you are talking about the numerical type, derivation is pretty straightforward: f'(x) = (f(x+epsilon) - f(x-epsilon))/(2*epsilon). If your function is regular enough, 2D integration can be done easily by the trapeze method. But you can check the link given by dudurocha.

Now if you are interested in the symbolic type, the differentiation is not too hard on Lisp, but integration is. But doing that in C must not be straightforward.

You might want to refer to the book "Numerical Recipes in C."

Thank u everyone for ur kind rply.