intergrals calculus

Question

If 𝑓(𝑥)f(x) is a positive continuous function on ℝR, what does the function 𝐹(𝑥)=∫𝑥𝑎𝑓(𝑡)𝑑𝑡F(x)=∫axf(t)dt represent (for 𝑥>𝑎)x>a)?

a. The slope of the tangent line to the graph of 𝑓f at 𝑥x.

b. The area between the graph of 𝑓(𝑥)f(x) and the 𝑦y-axis between 𝑓(𝑎)f(a) and 𝑓(𝑥)f(x).

c. The area between the graph of 𝑓f on the 𝑥x-axis on the interval [𝑎,𝑥][a,x].

d. The area of a rectangle with base on the horizontal axis.

Answer 1

Using Desmos to demonstrate:

desmos.com/calculator/jtuupsqg5e