Integration is simply the calculation of an integral. Integrals as a solution to differential functions that have undergone integration can be classified into two, namely the Definite and Indefinite Integral.
When we refer to the application of integrals, it usually pertains to the utilization of Definite integrals. Definite integrals result from integrating functions with defined boundaries (limits), integrals that result in specific values. However, we will focus on this notion in later chapters of this course.
On the other hand, Indefinite integrals do not contain defined boundaries; hence, the result of the integration process is a function of the given variable.
$\tcAal{Definite Integrals}$ $$\int_2^5 (x^2-2x+5) \,dx$$ $$\int_1^3 (4x+3) \,dx = 22 $$
$\tcAal{Indefinite Integrals}$ $$\int (x^2-2x+5) \,dx$$ $$\int (4x+3) \,dx = 2x^2+3x+C $$