Consider the following differential equation \begin{equation} p(t) = \frac{\partial q(t)}{\partial t} \end{equation} where $t \in (0,\infty)$. I have a build a code that spits out values of the function $p$ for the variable $t$.

Now, I'm looking for a scheme that will analyse these values of $p$ in order to determine $q$. Does anybody have any suggestions? The main problem is that if I would calculate $q(t) = \int p(t) \; \mathrm{d}t$, then I'll end up with just a number (i.e. the area under the graph), but I need to know the actual function of $q(t)$.

I've cross-posted this question here: http://math.stackexchange.com/questions/1326854/looking-for-a-particular-algorithm-for-numerical-integration#comment2695909_1326854

Consider the following differential equation \begin{equation} p(t) = \frac{\partial q(t)}{\partial t} \end{equation} where $t \in (0,\infty)$. I have a build a code that spits out values of the function $p$ for the variable $t$.

Now, I'm looking for a scheme that will analyse these values of $p$ in order to determine $q$. Does anybody have any suggestions? The main problem is that if I would calculate $q(t) = \int p(t) \; \mathrm{d}t$, then I'll end up with just a number (i.e. the area under the graph), but I need to know the actual function of $q(t)$.

I've cross-posted this question here: https://math.stackexchange.com/questions/1326854/looking-for-a-particular-algorithm-for-numerical-integration#comment2695909_1326854