Let $V=\mathrm{C}^0[a, b]$ be the vector space consisting of all functions $f(t)$ that are defined and continuous on the interval $0 \leq t \leq 1$. Which of the following conditions define subspaces of $V$ ? Explain your answer. (a) $f(0)=0$, (b) $f(0)=2 f(1),(c) f(0) f(1)=1$,
(d) $f(0)=0$ or $f(1)=0$,
(e) $f(1-t)=-t f(t)$,
(f) $f(1-t)=1-f(t)$,
(g) $f\left(\frac{1}{2}\right)=\int_0^1 f(t) d t$,
(h) $\int_0^1(t-1) f(t) d t=0$,
(i) $\int_0^t f(s) \sin s d s=\sin t$.