High School Calculus/Evaluating Definite Integrals

Evaluating a Definite Integral
Let's say you have the parabola $$x^2$$ and you want to find the area from x=2 to x=4 $$2 \leq A \leq 4$$ $$\int_{2}^{4}x^2\,dx$$ In order to take the integral of the function you have to do the opposite that of the derivative The power of the variable x will have a number added to it. So, $$x^{(a+1)}$$ then the number gets inverted and brought out front. $$\frac{1}{a+1} * x^{(a+1)}$$ $$\int_{2}^{4}x^{2}\, dx$$ From here we integrate and plug (b) into the indefinite integral and subtract the integral from (a) plugged into the indefinite integral. $$[\frac{1}{3}*4^{3}]-[\frac{1}{3}*2^{3}]$$ Now we evaluate the integral $$[\frac{1}{3}*64]-[\frac{1}{3}*8]$$ $$[\frac{64}{3}]-[\frac{8}{3}]$$ $$\frac{56}{3}$$ $$\frac{56}{3}$$ is the area underneath the curve from 2 to 4. In other words $$2 \leq A \leq 4$$