Evaluate the line integral given along the curve C

Evaluate the line integral given along the curve C
Calvin the Calculator, amidst his analytical endeavors aboard the MTheory Laboratory Spaceship, encounters a fascinating geometric puzzle. Tasked with determining the area of a region bound by the curve C using Green's Theorem, he visualizes the problem as a celestial field, where each point represents a star, and the curve C forms the boundary of a nebula. Utilizing the spaceship's advanced computational tools, he translates the swirling mass of cosmic dust into a mathematical model, applying Green’s Theorem to ingeniously calculate the area as an integral, transforming the abstract beauty of the cosmos into precise numerical truth.

[@user-dz3gx1ki2h]

اسلوب الحل غريب بما انى فى مصر و الصف النهائي من الثانويه ف اظن ان التكامل عندنا سهل تقريبا ... ممكن يكون ده مستوا عالى من دروس التكامل؟

[@mtheorylaboratory]

Hey! As far as I know this is the solution given in the textbook.. but there are 2 ways to solve the integral: long division or simplification :)