Solve the following integral: ∫(2x^3 + 5x^2 - 3x + 4) dx

Remember to use the power rule for integration and follow the steps to find the antiderivative of the function.

Given the function G(x) where we denote it's derivative as , looking at the definitions that have been assigned to the individual functions, show what integrating the following integral would give us  

12. Exactly how many of the following four mathematical statements are always true: (i) The definite integral represents area under a curve or beneath a curve. (ii) The definite integral is a function obtained by taking the limit of a special sum. (iii) The definite integral of a function g(x) is a function G() such that G(x) dx = g(x) e is defined to be F(b) - F(a) where F is any antiderivative of (a) 4 (b) 3 (c) 2 (d) 1 (e) o

Evaluate the indefinite integral. Illustrate and check that your answer is reasonable by graphing both the function and its antiderivative (take).