$\lim\limits_{x\to 1}\bigg[\large\frac{x^3+2x^2+x+1}{x^2+2x+3}\bigg]^{\Large\frac{1-\cos(x-1)}{(x-1)^2}}$

Question

$(a)\;e\qquad(b)\;e^{\Large\frac{1}{2}}\qquad(c)\;1\qquad(d)\;\sqrt{\large\frac{5}{6}}$