Redefining the Integral

In this talk, we will discuss a ''new'' way to define an integral. Instead of using the standard definition of $\displaystyle \sum_{i=1}^{n} f(x_{i}) \hspace{3pt} \Delta x_{i}$, can we use an infinite product? How will this change the definition of an integral? Will this also change the definition of a derivative? This talk will examine the new mysteries of the so-called ''star-integral'' and ''star-derivative''.