Constant of integration

A constant which forms part of the general integral of a function. The point here is that any function has a whole family of integrals. The simplest integral is the simplest of them all, but all the others differ from that one by a constant. The general integral of a function f can be summed up in a single statement:

I(x) + C

where I(x) is the simplest integral of f(x), and C is any constant. C is known as the arbitary constant of integration. The derivative of this is:

d/dx(I(x) + C)
= d/dx(I(x)) (sum rule in differentiation, derivative of a constant)
= f(x)

as required.