Find dz/dy and dz/dx

Question

Let z = ∫e^(sin(t))dt from x to y

a = x
b = y

I tried thinking about it like a chain rule but even then i'm a little unsure.

I know dz/dt = e^(sin(t)). Can you please point me in the right direction if i'm supposed to use the chain rule.

Answer 1

if F = Integral(f(t)) [x,y] then
dF/dx = f(x) = e^sin(x)
dF/dy = -f(y) = -e^sin(y)

wikipedia has a good article on differentiation under the integral