Question: Evaluate the definite integral of the function f(x) = 2x + 3 from x = 1 to x = 5.

Answer: To evaluate the definite integral of the given function f(x) = 2x + 3 from x = 1 to x = 5, we use the definite integral formula:

∫[1 to 5] (2x + 3) dx

First, we find the indefinite integral:

∫(2x + 3) dx = x^2 + 3x + C

Now, we can evaluate the definite integral by applying the fundamental theorem of calculus:

= [x^2 + 3x] from 1 to 5 = (5^2 + 35) - (1^2 + 31) = (25 + 15) - (1 + 3) = 40 - 4 = 36

Therefore, the definite integral of the function f(x) = 2x + 3 from x = 1 to x = 5 is 36.