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plotting - Plot a function after taking the supremum with respect to one variable


Assume given a continuous function $f$ with 2 variables, say $x$ and $y$. $x$ takes values on the interval $I$ and $y$ takes values on the interval $J$. I would like to know how to plot the function $$g(y):=\sup_{x\in I}f(x,y)$$ using Mathematica. For example, $f(x,y)=e^y\sin(x^2)$ with $x\in[0,1], y\in[0,1]$. Many thanks.




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