Use maple lab and maple commands to solve the following .

Problem # 1 For each function fx) given below, define Fox)- a f(t) dt. 1) Is F(x) an antiderivative of fix)? 2) Plot fix) and F(x) in the same window for xe [a, b]. 3) How is F(x) related to the area between f(x) and the x-axis on[a, b]? (a) fx)a-1,b 10 (b) f(x) - sin x, a 0, b-Im (c)f(x)-1x4-2x3 + 4 x2, a = 0, b-5 (d) fix) = 4x4-2x3 +4x2, a = 0, b = 6 Problem # 2 The integral Jt Vx +I dx represents the area A of a region in the first quadrant. (a) Find the exact area A. (b) Approximate A, using the following partitions: 1. n 10 2. n 100 3.n 1000 Which of these three will give the best answer? Usem 10 and then 100 (e) Work this problem by finding Sn)-(c)Ax where c is the right endpoint, and taking the limit as n approaches infinity. How does this result compare to the one obtained in (a)? (d) Can you approximate A to a precision of two decimal places? Three decimal places? (c) Tocheck your answer in part (d) enter the command evalf (Int( )) fneeded