设f(x)连续且满足f(x)=-cosx+∫x0f(t)dt，求f(x)．

设f(x)连续且满足f(x)=-cosx+∫x0f(t)dt，求f(x)．
【正确答案】：先证f(x)可导．f(x)=-(1/2)(ex+sinx+cosx)．