Integration is the opposite of differentiating. An integral is essentially asking ‘What function am I the derivative of?’. It’s like working backwards from the derivative to find the original function. An antiderivative equation is essentially undoing a derivative. The antiderivative of an equation is the equation that you would take the derivative of to get the function you already have. Since we have two equations, we will need to find two separate antide- rivative equations. The great thing about integrals is you can always check your answer, by taking the derivative of your answer.
When you don’t have a set integral, your answer will always be a function. Because there are no boundaries, there are an infinite number of antiderivatives for any given function. We include these into our answers by including ‘+c’. ‘C’ represents any real number. If you think about this in terms of derivatives, when you take the derivative of a function you drop any constant. How- ever, to get back to that original function we must make sure we include that constant, which is why we add +c.
If you are given a particular value, sometimes you have to solve for c.