If for a continuous function f(x) , $\;\int \limits_{\pi}^{t} (f(x)+x) dx = \pi^{2}-t^{2}\;$ , for all $\;t \geq -\pi\;$ , then $\;f(- \large\frac{\pi}{3})\;$ is equal to :

Question

$(a)\;\pi\qquad(b)\;\large\frac{\pi}{2} \qquad(c)\;\large\frac{\pi}{3}\qquad(d)\;\large\frac{\pi}{6}$