Integral
The  at the end is what shows that we are integrating with respect to x, that is, as x changes. This can be seen to be the inverse of differentiation. However, there is a constant, C, added when integrating. This is called the constant of integration. This is required because differentiating an integer results in zero, therefore integrating zero (which can be put onto the end of any integrand) produces an integer, C. The value of this integer would be found by using given conditions.