Line Integral

The following problem is supposed to be solved using line integral ( as indicated in the example), but I can't find any parametrization of y=x^3 that makes my integral solvable by hand and I am unclear about the bound of t.

Please help me out.

Problem:

Find the area of the wall whose base is the part of the curve y = :53 in the any-plane going from (0,0) to (1,1) and Whose height at point (any) is given by f(:c,y) = 273;, with units measured in meters. Example 1.1.3. Let C be the portion of the ellipse $42 + % = 1 in the rst quadrant. Suppose we have a fence whose base lies along the curve C in the anyplane and whose height at any point (:13, y) on C is given by f (53,31) 2 my. Find the area of the fence. Z Solution: We begin by parametrizationC by r(t) = (2 cost, 4sint) for 0