Integrating integrals at intervals within an integrated idea of infinity

The end of the year has arrived and I have spent the past term in a workshop called Intro to Calculus. We have spent this time learning the basics of calculus including limits, derivatives, and integrals. For my final action project in this class we were tasked to create a function and find the area underneath it using Riemann sums and integrals. The two numbers I was given to create a function were -8 and 10. With them I created the function f(x)=-8sin(x)+10x and I chose to find the area underneath it when 0<x<1.25.

    As we finish up this intro to calculus workshop, Ive reflected on what the meaning of calculus is. In a literal sense it is a branch of mathematics. But it can also be so much more. The basis of calculus is the idea of infinity. Functions can continue on for infinite lengths. The value of f(x) will get infinitely smaller as a function approaches its limit. Derivatives is finding the slope of a point at a function with points that are infinitely closer together. All the concepts of calculus involve infinity and I think that is the most important part of it all. The meaning of calculus can be simple in a mathematic way but complex as you expand your view and think about what infinity means.