Please help me with the following questions.

1.

Guess an antiderivative for the integrand function. Validate your guess by differentiation and then evaluate the given definite integral. (Hint: Keep in mind the Chain Rule in guessing an antiderivative.) 3 x dx 2 1/4 + x 2 3 x dx 2 1/4+ x 2 (Type an exact answer, using radicals as needed.)62 Use the rules for definite integration and the formulas | cdx = c(b - a) for any constant c and xdx _ a 2 for b > a to evaluate the integral ( 6t - 1 ) dt . a N ( 6t - 1 ) dt = 1 (Simplify your answer.)Use finite approximations to estimate the area under the graph of the function f(x) = 25 - x between x - -5 and x = 5 for each of the following cases. a. Using a lower sum with two rectangles of equal width b. Using a lower sum with four rectangles of equal width c. Using an upper sum with two rectangles of equal width d. Using an upper sum with four rectangles of equal width a. The area under the graph of f(x) using a lower sum with two rectangles of equal width is (Type an integer or a decimal.) b. The area under the graph of f(x) using a lower sum with four rectangles of equal width is (Type an integer or a decimal.) c. The area under the graph of f(x) using an upper sum with two rectangles of equal width is (Type an integer or a decimal.) d. The area under the graph of f(x) using an upper sum with four rectangles of equal width is . (Type an integer or a decimal.) Ti W O