# Finding the sketch of the original function from a sketch of its derivative

Let's just say I had a graph like the one above but I didn't know its equation. Let's also say it's the graph of a derivative function and I had to find the graph of the original function between x = -2 and x = 4. How would finding the area underneath the graph, between these two points help me to sketch the original function?

NOTE: I have a homework question very similar to this but with a different graph. I just wanted to figure out or understand the method behind how finding the area underneath the derivative function between these two points can help with the sketch of the original function.

• Roughly speaking, the area under your plotted curve is the integral of that curve, up to a constant value. I found the YouTube series Essense of Calculus by 3Blue1Brown is helpful for beginning to understand calculus. – Samadin May 13 '17 at 14:29

• @user411697 I would first notice that $f(0) = f^{\prime} (0) = 0$ because area under that is zero. Then I would find $\int_{0}^{t} f^{\prime}(x) dx = f(t)$ for all $t \geqslant -2$ and $t \leqslant 4$. Then I would just make a table and plot those points and approximate the original function. – Sadij May 13 '17 at 14:59