A function g is defined by g(x)=∫0xf(t)dt, where f is continuous. At x=5, one has f(5)=0, with f(t)<0 for t<5 sufficiently close to 5 and f(t)>0 for t>5 sufficiently close to 5. Which statement best describes the behavior of g at x=5?
a) g has a local maximum at x=5.
b) g has a point of inflection at x=5.
c) g has a local minimum at x=5.
d) g is neither increasing nor decreasing near x=5.